# Chinese Wooden Puzzles in N by 8

Below the results for the Chinese Wooden Puzzle that fit in a frame of size
N by 8 for all possible values for N and combination of
kind of pieces, where 4 pieces of each selected kind are used.
This page is generated with the program genCWP10.cpp
## Chinese Wooden Puzzles in 1 by 8

The one solution is symmetric in two directions.
The one pattern is:

## Chinese Wooden Puzzles in 2 by 8

The one normalized solution is not symmetric in any direction.
The one pattern is:

The one solution is symmetric in two directions.
The one pattern is:

The one solution is symmetric in two directions.
The one pattern is:

## Chinese Wooden Puzzles in 3 by 8

Two normalized solutions are not symmetric in any direction.
There is one minimal touching pattern, which is suboptimal with five extra.
There is one maximal touching pattern.
The patterns are:

Six normalized solutions are symmetric in one direction.
31 normalized solutions are not symmetric in any direction.
Eight solutions (two normalized solutions) are permutations of four solutions of blue, one solution of purple.
This leaves 128 mix solutions.
One pattern is a combination of two smaller patterns.
13 patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with one extra.
There is one maximal touching pattern.
The patterns are:

The one normalized solution is symmetric in one direction.
Two solutions (one normalized solution) are permutations of one solution of green, one solution of purple.
There are no mix solutions.
All patterns are a combination of two smaller patterns.
The one pattern is:

One normalized solution is symmetric in one direction.
Five normalized solutions are not symmetric in any direction.
Two solutions (one normalized solution) are permutations of one solution of black, one solution of purple.
This leaves 20 mix solutions.
One pattern is a combination of two smaller patterns.
One pattern is a mix patterns.
There is one minimal touching pattern, which is suboptimal with seven extra.
There is one maximal touching pattern.
The patterns are:

## Chinese Wooden Puzzles in 4 by 8

Ten normalized solutions are not symmetric in any direction.
The one pattern is:

The one normalized solution is not symmetric in any direction.
The one pattern is:

11 normalized solutions are not symmetric in any direction.
Eight solutions (two normalized solutions) are permutations of one solution of green, four solutions of blue.
This leaves 36 mix solutions.
One pattern is a combination of two smaller patterns.
Two patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with ten extra.
There is one maximal touching pattern.
The patterns are:

Two normalized solutions are not symmetric in any direction.
The one pattern is:

One normalized solution is symmetric in one direction.
26 normalized solutions are not symmetric in any direction.
Eight solutions (two normalized solutions) are permutations of one solution of black, four solutions of blue.
This leaves 98 mix solutions.
One pattern is a combination of two smaller patterns.
Nine patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with six extra.
There is one maximal touching pattern.
The patterns are:

Two normalized solutions are symmetric in one direction.
Two normalized solutions are not symmetric in any direction.
Two solutions (one normalized solution) are permutations of one solution of black, one solution of green.
This leaves ten mix solutions.
One pattern is a combination of two smaller patterns.
Three patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with six extra.
There is one maximal touching pattern.
The patterns are:

## Chinese Wooden Puzzles in 5 by 8

Six normalized solutions are not symmetric in any direction.
There is one minimal touching pattern, which is suboptimal with eight extra.
There are two maximal touching patterns.
The patterns are:

32 normalized solutions are not symmetric in any direction.
There are four minimal touching patterns, which are suboptimal with seven extra.
There is one maximal touching pattern.
The patterns are:

857 normalized solutions are not symmetric in any direction.
64 solutions (16 normalized solutions) are permutations of eight solutions of yellow and purple, four solutions of blue.
80 solutions (20 normalized solutions) are permutations of 40 solutions of yellow and blue, one solution of purple.
There are a total of 144 solutions (36 normalized solutions) that are permutations, leaving 3,284 mix solutions.
Five patterns are a combination of two smaller patterns.
246 patterns are a mix patterns.
There are three minimal touching patterns, which are suboptimal with four extra.
There are two maximal touching patterns.
The patterns are:

Seven normalized solutions are not symmetric in any direction.
16 solutions (four normalized solutions) are permutations of eight solutions of yellow and purple, one solution of green.
Eight solutions (two normalized solutions) are permutations of four solutions of yellow and green, one solution of purple.
There are a total of 24 solutions (six normalized solutions) that are permutations, leaving four mix solutions.
Five patterns are a combination of two smaller patterns.
One pattern is a mix patterns.
There are two minimal touching patterns, which are suboptimal with eight extra.
There is one maximal touching pattern.
The patterns are:

12 normalized solutions are symmetric in one direction.
340 normalized solutions are not symmetric in any direction.
256 solutions (64 normalized solutions) are permutations of 128 solutions of blue and purple, one solution of green.
72 solutions (18 normalized solutions) are permutations of 36 solutions of blue and green, one solution of purple.
There are a total of 328 solutions (82 normalized solutions) that are permutations, leaving 1,056 mix solutions.
29 patterns are a combination of two smaller patterns.
Three patterns are a combination of three smaller patterns.
62 patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with two extra.
There are two maximal touching patterns.
The patterns are:

245 normalized solutions are not symmetric in any direction.
16 solutions (four normalized solutions) are permutations of eight solutions of yellow and purple, one solution of black.
16 solutions (four normalized solutions) are permutations of eight solutions of yellow and black, one solution of purple.
There are a total of 32 solutions (eight normalized solutions) that are permutations, leaving 948 mix solutions.
Five patterns are a combination of two smaller patterns.
104 patterns are a mix patterns.
There are four minimal touching patterns, which are suboptimal with five extra.
There are two maximal touching patterns.
The patterns are:

29 normalized solutions are symmetric in one direction.
4,320 normalized solutions are not symmetric in any direction.
256 solutions (64 normalized solutions) are permutations of 128 solutions of blue and purple, one solution of black.
160 solutions (40 normalized solutions) are permutations of 20 solutions of black and purple, four solutions of blue.
196 solutions (49 normalized solutions) are permutations of 98 solutions of blue and black, one solution of purple.
There are a total of 612 solutions (153 normalized solutions) that are permutations, leaving 16,726 mix solutions.
44 patterns are a combination of two smaller patterns.
Three patterns are a combination of three smaller patterns.
946 patterns are a mix patterns.
There are three optimal minimal touching patterns.
There are three maximal touching patterns.
The patterns are:

Three normalized solutions are symmetric in one direction.
120 normalized solutions are not symmetric in any direction.
40 solutions (ten normalized solutions) are permutations of 20 solutions of black and purple, one solution of green.
20 solutions (five normalized solutions) are permutations of ten solutions of green and black, one solution of purple.
There are a total of 60 solutions (15 normalized solutions) that are permutations, leaving 426 mix solutions.
Six patterns are a combination of two smaller patterns.
Three patterns are a combination of three smaller patterns.
35 patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with three extra.
There are two maximal touching patterns.
The patterns are:

## Chinese Wooden Puzzles in 6 by 8

16 normalized solutions are not symmetric in any direction.
There are three minimal touching patterns, which are suboptimal with ten extra.
There are two maximal touching patterns.
The patterns are:

75 normalized solutions are not symmetric in any direction.
80 solutions (20 normalized solutions) are permutations of 40 solutions of yellow and blue, one solution of green.
32 solutions (eight normalized solutions) are permutations of four solutions of yellow and green, four solutions of blue.
There are a total of 112 solutions (28 normalized solutions) that are permutations, leaving 188 mix solutions.
Two patterns are a combination of two smaller patterns.
15 patterns are a mix patterns.
There are three minimal touching patterns, which are suboptimal with 11 extra.
There are two maximal touching patterns.
The patterns are:

11 normalized solutions are not symmetric in any direction.
There is one minimal touching pattern, which is suboptimal with nine extra.
There is one maximal touching pattern.
The patterns are:

241 normalized solutions are not symmetric in any direction.
80 solutions (20 normalized solutions) are permutations of 40 solutions of yellow and blue, one solution of black.
64 solutions (16 normalized solutions) are permutations of eight solutions of yellow and black, four solutions of blue.
There are a total of 144 solutions (36 normalized solutions) that are permutations, leaving 820 mix solutions.
Two patterns are a combination of two smaller patterns.
85 patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with five extra.
There are two maximal touching patterns.
The patterns are:

14 normalized solutions are not symmetric in any direction.
Eight solutions (two normalized solutions) are permutations of four solutions of yellow and green, one solution of black.
16 solutions (four normalized solutions) are permutations of eight solutions of yellow and black, one solution of green.
There are a total of 24 solutions (six normalized solutions) that are permutations, leaving 32 mix solutions.
Two patterns are a combination of two smaller patterns.
Four patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with 16 extra.
There are two maximal touching patterns.
The patterns are:

Six normalized solutions are symmetric in one direction.
377 normalized solutions are not symmetric in any direction.
72 solutions (18 normalized solutions) are permutations of 36 solutions of blue and green, one solution of black.
196 solutions (49 normalized solutions) are permutations of 98 solutions of blue and black, one solution of green.
80 solutions (20 normalized solutions) are permutations of ten solutions of green and black, four solutions of blue.
There are a total of 348 solutions (87 normalized solutions) that are permutations, leaving 1,172 mix solutions.
23 patterns are a combination of two smaller patterns.
Three patterns are a combination of three smaller patterns.
118 patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with two extra.
There are three maximal touching patterns.
The patterns are:

18 normalized solutions are not symmetric in any direction.
There is one minimal touching pattern, which is suboptimal with nine extra.
There are two maximal touching patterns.
The patterns are:

## Chinese Wooden Puzzles in 7 by 8

10,875 normalized solutions are not symmetric in any direction.
192 solutions (48 normalized solutions) are permutations of 24 solutions of red, yellow, and purple, four solutions of blue.
128 solutions (32 normalized solutions) are permutations of 64 solutions of red, yellow, and blue, one solution of purple.
There are a total of 320 solutions (80 normalized solutions) that are permutations, leaving 43,180 mix solutions.
28 patterns are a combination of two smaller patterns.
4,181 patterns are a mix patterns.
Too many patterns to display them all.
The one suboptimal (four extra) minimal touching pattern is:

22 normalized solutions are not symmetric in any direction.
48 solutions (12 normalized solutions) are permutations of 24 solutions of red, yellow, and purple, one solution of green.
This leaves 40 mix solutions.
Ten patterns are a combination of two smaller patterns.
Seven patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with ten extra.
There is one maximal touching pattern.
The patterns are:

355 normalized solutions are not symmetric in any direction.
256 solutions (64 normalized solutions) are permutations of 128 solutions of red, blue, and purple, one solution of green.
This leaves 1,164 mix solutions.
34 patterns are a combination of two smaller patterns.
162 patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with six extra.
There are four maximal touching patterns.
The patterns are:

6,129 normalized solutions are not symmetric in any direction.
240 solutions (60 normalized solutions) are permutations of 40 solutions of yellow and blue, one solution of green, one solution of purple.
96 solutions (24 normalized solutions) are permutations of four solutions of yellow and green, four solutions of blue, one solution of purple.
1,024 solutions (256 normalized solutions) are permutations of four solutions of yellow and green, 128 solutions of blue and purple.
576 solutions (144 normalized solutions) are permutations of 36 solutions of blue and green, eight solutions of yellow and purple.
6,568 solutions (1,642 normalized solutions) are permutations of 3,284 solutions of yellow, blue, and purple, one solution of green.
32 solutions (eight normalized solutions) are permutations of four solutions of yellow, green, and purple, four solutions of blue.
376 solutions (94 normalized solutions) are permutations of 188 solutions of yellow, blue, and green, one solution of purple.
There are a total of 8,912 solutions (2,228 normalized solutions) that are permutations, leaving 15,604 mix solutions.
588 patterns are a combination of two smaller patterns.
18 patterns are a combination of three smaller patterns.
1,379 patterns are a mix patterns.
Too many patterns to display them all.
The 19 suboptimal (seven extra) minimal touching patterns are:

One normalized solution is symmetric in one direction.
239 normalized solutions are not symmetric in any direction.
48 solutions (12 normalized solutions) are permutations of 24 solutions of red, yellow, and purple, one solution of black.
This leaves 910 mix solutions.
Ten patterns are a combination of two smaller patterns.
133 patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with seven extra.
There is one maximal touching pattern.
The patterns are:

2,886 normalized solutions are not symmetric in any direction.
256 solutions (64 normalized solutions) are permutations of 128 solutions of red, blue, and purple, one solution of black.
88 solutions (22 normalized solutions) are permutations of 44 solutions of red, blue, and black, one solution of purple.
There are a total of 344 solutions (86 normalized solutions) that are permutations, leaving 11,200 mix solutions.
56 patterns are a combination of two smaller patterns.
1,171 patterns are a mix patterns.
There are three minimal touching patterns, which are suboptimal with four extra.
There are two maximal touching patterns.
The patterns are:

41,866 normalized solutions are not symmetric in any direction.
240 solutions (60 normalized solutions) are permutations of 40 solutions of yellow and blue, one solution of black, one solution of purple.
1,600 solutions (400 normalized solutions) are permutations of 40 solutions of yellow and blue, 20 solutions of black and purple.
192 solutions (48 normalized solutions) are permutations of eight solutions of yellow and black, four solutions of blue, one solution of purple.
2,048 solutions (512 normalized solutions) are permutations of eight solutions of yellow and black, 128 solutions of blue and purple.
1,568 solutions (392 normalized solutions) are permutations of 98 solutions of blue and black, eight solutions of yellow and purple.
6,568 solutions (1,642 normalized solutions) are permutations of 3,284 solutions of yellow, blue, and purple, one solution of black.
7,584 solutions (1,896 normalized solutions) are permutations of 948 solutions of yellow, black, and purple, four solutions of blue.
1,640 solutions (410 normalized solutions) are permutations of 820 solutions of yellow, blue, and black, one solution of purple.
There are a total of 21,440 solutions (5,360 normalized solutions) that are permutations, leaving 146,024 mix solutions.
1,009 patterns are a combination of two smaller patterns.
18 patterns are a combination of three smaller patterns.
10,914 patterns are a mix patterns.
Too many patterns to display them all.
The three suboptimal (five extra) minimal touching patterns are:

1,287 normalized solutions are not symmetric in any direction.
24 solutions (six normalized solutions) are permutations of four solutions of yellow and green, one solution of black, one solution of purple.
160 solutions (40 normalized solutions) are permutations of four solutions of yellow and green, 20 solutions of black and purple.
48 solutions (12 normalized solutions) are permutations of eight solutions of yellow and black, one solution of green, one solution of purple.
160 solutions (40 normalized solutions) are permutations of ten solutions of green and black, eight solutions of yellow and purple.
Eight solutions (two normalized solutions) are permutations of four solutions of yellow, green, and purple, one solution of black.
1,896 solutions (474 normalized solutions) are permutations of 948 solutions of yellow, black, and purple, one solution of green.
64 solutions (16 normalized solutions) are permutations of 32 solutions of yellow, green, and black, one solution of purple.
There are a total of 2,360 solutions (590 normalized solutions) that are permutations, leaving 2,788 mix solutions.
246 patterns are a combination of two smaller patterns.
18 patterns are a combination of three smaller patterns.
331 patterns are a mix patterns.
There are five minimal touching patterns, which are suboptimal with seven extra.
There is one maximal touching pattern.
The patterns are:

76 normalized solutions are symmetric in one direction.
38,845 normalized solutions are not symmetric in any direction.
216 solutions (54 normalized solutions) are permutations of 36 solutions of blue and green, one solution of black, one solution of purple.
1,440 solutions (360 normalized solutions) are permutations of 36 solutions of blue and green, 20 solutions of black and purple.
588 solutions (147 normalized solutions) are permutations of 98 solutions of blue and black, one solution of green, one solution of purple.
240 solutions (60 normalized solutions) are permutations of ten solutions of green and black, four solutions of blue, one solution of purple.
2,560 solutions (640 normalized solutions) are permutations of ten solutions of green and black, 128 solutions of blue and purple.
2,112 solutions (528 normalized solutions) are permutations of 1,056 solutions of blue, green, and purple, one solution of black.
33,452 solutions (8,363 normalized solutions) are permutations of 16,726 solutions of blue, black, and purple, one solution of green.
3,408 solutions (852 normalized solutions) are permutations of 426 solutions of green, black, and purple, four solutions of blue.
2,344 solutions (586 normalized solutions) are permutations of 1,172 solutions of blue, green, and black, one solution of purple.
There are a total of 46,360 solutions (11,590 normalized solutions) that are permutations, leaving 109,172 mix solutions.
2,516 patterns are a combination of two smaller patterns.
153 patterns are a combination of three smaller patterns.
12 patterns are a combination of four smaller patterns.
6,492 patterns are a mix patterns.
Too many patterns to display them all.
The one suboptimal (one extra) minimal touching pattern is:

55 normalized solutions are not symmetric in any direction.
There are two minimal touching patterns, which are suboptimal with nine extra.
There is one maximal touching pattern.
The patterns are:

169 normalized solutions are not symmetric in any direction.
There is one minimal touching pattern, which is suboptimal with seven extra.
There is one maximal touching pattern.
The patterns are:

3,191 normalized solutions are not symmetric in any direction.
144 solutions (36 normalized solutions) are permutations of 72 solutions of orange, blue, and white, one solution of purple.
This leaves 12,620 mix solutions.
20 patterns are a combination of two smaller patterns.
1,089 patterns are a mix patterns.
There are two optimal minimal touching patterns.
There are four maximal touching patterns.
The patterns are:

Eight normalized solutions are not symmetric in any direction.
There is one minimal touching pattern, which is suboptimal with 11 extra.
There is one maximal touching pattern.
The patterns are:

Two normalized solutions are symmetric in one direction.
117 normalized solutions are not symmetric in any direction.
There is one minimal touching pattern, which is suboptimal with five extra.
There is one maximal touching pattern.
The patterns are:

## Chinese Wooden Puzzles in 8 by 8

102 normalized solutions are not symmetric in any direction.
128 solutions (32 normalized solutions) are permutations of 64 solutions of red, yellow, and blue, one solution of green.
This leaves 280 mix solutions.
18 patterns are a combination of two smaller patterns.
42 patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with nine extra.
There are eight maximal touching patterns.
The patterns are:

1,538 normalized solutions are not symmetric in any direction.
128 solutions (32 normalized solutions) are permutations of 64 solutions of red, yellow, and blue, one solution of black.
This leaves 6,024 mix solutions.
18 patterns are a combination of two smaller patterns.
896 patterns are a mix patterns.
There are four minimal touching patterns, which are suboptimal with six extra.
There are eight maximal touching patterns.
The patterns are:

180 normalized solutions are not symmetric in any direction.
88 solutions (22 normalized solutions) are permutations of 44 solutions of red, blue, and black, one solution of green.
This leaves 632 mix solutions.
22 patterns are a combination of two smaller patterns.
124 patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with nine extra.
There are four maximal touching patterns.
The patterns are:

3,002 normalized solutions are not symmetric in any direction.
192 solutions (48 normalized solutions) are permutations of eight solutions of yellow and black, one solution of green, four solutions of blue.
576 solutions (144 normalized solutions) are permutations of eight solutions of yellow and black, 36 solutions of blue and green.
784 solutions (196 normalized solutions) are permutations of 98 solutions of blue and black, four solutions of yellow and green.
800 solutions (200 normalized solutions) are permutations of ten solutions of green and black, 40 solutions of yellow and blue.
376 solutions (94 normalized solutions) are permutations of 188 solutions of yellow, blue, and green, one solution of black.
1,640 solutions (410 normalized solutions) are permutations of 820 solutions of yellow, blue, and black, one solution of green.
256 solutions (64 normalized solutions) are permutations of 32 solutions of yellow, green, and black, four solutions of blue.
There are a total of 4,624 solutions (1,156 normalized solutions) that are permutations, leaving 7,384 mix solutions.
249 patterns are a combination of two smaller patterns.
Nine patterns are a combination of three smaller patterns.
676 patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with seven extra.
There are six maximal touching patterns.
The patterns are:

12 normalized solutions are not symmetric in any direction.
There are two minimal touching patterns, which are suboptimal with 14 extra.
There are two maximal touching patterns.
The patterns are:

96 normalized solutions are not symmetric in any direction.
There are two minimal touching patterns, which are suboptimal with ten extra.
There are two maximal touching patterns.
The patterns are:

Two normalized solutions are symmetric in one direction.
472 normalized solutions are not symmetric in any direction.
There are two minimal touching patterns, which are suboptimal with eight extra.
There are four maximal touching patterns.
The patterns are:

122 normalized solutions are not symmetric in any direction.
144 solutions (36 normalized solutions) are permutations of 72 solutions of orange, blue, and white, one solution of green.
This leaves 344 mix solutions.
20 patterns are a combination of two smaller patterns.
46 patterns are a mix patterns.
There are six minimal touching patterns, which are suboptimal with ten extra.
There are four maximal touching patterns.
The patterns are:

16 normalized solutions are not symmetric in any direction.
There are two minimal touching patterns, which are suboptimal with 12 extra.
There are two maximal touching patterns.
The patterns are:

34 normalized solutions are not symmetric in any direction.
There are two minimal touching patterns, which are suboptimal with 13 extra.
There are two maximal touching patterns.
The patterns are:

658 normalized solutions are not symmetric in any direction.
144 solutions (36 normalized solutions) are permutations of 72 solutions of orange, blue, and white, one solution of black.
This leaves 2,488 mix solutions.
20 patterns are a combination of two smaller patterns.
298 patterns are a mix patterns.
There are four minimal touching patterns, which are suboptimal with nine extra.
There are two maximal touching patterns.
The patterns are:

## Chinese Wooden Puzzles in 9 by 8

61,572 normalized solutions are not symmetric in any direction.
576 solutions (144 normalized solutions) are permutations of 24 solutions of red, yellow, and purple, one solution of green, four solutions of blue.
1,728 solutions (432 normalized solutions) are permutations of 24 solutions of red, yellow, and purple, 36 solutions of blue and green.
1,024 solutions (256 normalized solutions) are permutations of 128 solutions of red, blue, and purple, four solutions of yellow and green.
384 solutions (96 normalized solutions) are permutations of 64 solutions of red, yellow, and blue, one solution of green, one solution of purple.
86,360 solutions (21,590 normalized solutions) are permutations of 43,180 solutions of red, yellow, blue, and purple, one solution of green.
320 solutions (80 normalized solutions) are permutations of 40 solutions of red, yellow, green, and purple, four solutions of blue.
560 solutions (140 normalized solutions) are permutations of 280 solutions of red, yellow, blue, and green, one solution of purple.
There are a total of 90,952 solutions (22,738 normalized solutions) that are permutations, leaving 155,336 mix solutions.
8,582 patterns are a combination of two smaller patterns.
84 patterns are a combination of three smaller patterns.
12,945 patterns are a mix patterns.
Too many patterns to display them all.
The one suboptimal (five extra) minimal touching pattern is:

Two normalized solutions are symmetric in one direction.
583,970 normalized solutions are not symmetric in any direction.
576 solutions (144 normalized solutions) are permutations of 24 solutions of red, yellow, and purple, one solution of black, four solutions of blue.
4,704 solutions (1,176 normalized solutions) are permutations of 24 solutions of red, yellow, and purple, 98 solutions of blue and black.
2,048 solutions (512 normalized solutions) are permutations of 128 solutions of red, blue, and purple, eight solutions of yellow and black.
384 solutions (96 normalized solutions) are permutations of 64 solutions of red, yellow, and blue, one solution of black, one solution of purple.
2,560 solutions (640 normalized solutions) are permutations of 64 solutions of red, yellow, and blue, 20 solutions of black and purple.
704 solutions (176 normalized solutions) are permutations of 44 solutions of red, blue, and black, eight solutions of yellow and purple.
86,360 solutions (21,590 normalized solutions) are permutations of 43,180 solutions of red, yellow, blue, and purple, one solution of black.
7,280 solutions (1,820 normalized solutions) are permutations of 910 solutions of red, yellow, black, and purple, four solutions of blue.
12,048 solutions (3,012 normalized solutions) are permutations of 6,024 solutions of red, yellow, blue, and black, one solution of purple.
There are a total of 116,664 solutions (29,166 normalized solutions) that are permutations, leaving 2,219,220 mix solutions.
10,963 patterns are a combination of two smaller patterns.
84 patterns are a combination of three smaller patterns.
193,101 patterns are a mix patterns.
Too many patterns to display them all.
The one suboptimal (three extra) minimal touching pattern is:

Two normalized solutions are symmetric in one direction.
3,413 normalized solutions are not symmetric in any direction.
144 solutions (36 normalized solutions) are permutations of 24 solutions of red, yellow, and purple, one solution of black, one solution of green.
480 solutions (120 normalized solutions) are permutations of 24 solutions of red, yellow, and purple, ten solutions of green and black.
80 solutions (20 normalized solutions) are permutations of 40 solutions of red, yellow, green, and purple, one solution of black.
1,820 solutions (455 normalized solutions) are permutations of 910 solutions of red, yellow, black, and purple, one solution of green.
There are a total of 2,524 solutions (631 normalized solutions) that are permutations, leaving 11,132 mix solutions.
352 patterns are a combination of two smaller patterns.
30 patterns are a combination of three smaller patterns.
1,650 patterns are a mix patterns.
Too many patterns to display them all.
The one suboptimal (six extra) minimal touching pattern is:

41,339 normalized solutions are not symmetric in any direction.
768 solutions (192 normalized solutions) are permutations of 128 solutions of red, blue, and purple, one solution of black, one solution of green.
2,560 solutions (640 normalized solutions) are permutations of 128 solutions of red, blue, and purple, ten solutions of green and black.
264 solutions (66 normalized solutions) are permutations of 44 solutions of red, blue, and black, one solution of green, one solution of purple.
2,328 solutions (582 normalized solutions) are permutations of 1,164 solutions of red, blue, green, and purple, one solution of black.
22,400 solutions (5,600 normalized solutions) are permutations of 11,200 solutions of red, blue, black, and purple, one solution of green.
1,264 solutions (316 normalized solutions) are permutations of 632 solutions of red, blue, green, and black, one solution of purple.
There are a total of 29,584 solutions (7,396 normalized solutions) that are permutations, leaving 135,772 mix solutions.
3,186 patterns are a combination of two smaller patterns.
168 patterns are a combination of three smaller patterns.
14,675 patterns are a mix patterns.
Too many patterns to display them all.
The eight suboptimal (five extra) minimal touching patterns are:

Two normalized solutions are symmetric in one direction.
634,472 normalized solutions are not symmetric in any direction.
19,704 solutions (4,926 normalized solutions) are permutations of 3,284 solutions of yellow, blue, and purple, one solution of black, one solution of green.
65,680 solutions (16,420 normalized solutions) are permutations of 3,284 solutions of yellow, blue, and purple, ten solutions of green and black.
96 solutions (24 normalized solutions) are permutations of four solutions of yellow, green, and purple, one solution of black, four solutions of blue.
784 solutions (196 normalized solutions) are permutations of four solutions of yellow, green, and purple, 98 solutions of blue and black.
16,896 solutions (4,224 normalized solutions) are permutations of 1,056 solutions of blue, green, and purple, eight solutions of yellow and black.
22,752 solutions (5,688 normalized solutions) are permutations of 948 solutions of yellow, black, and purple, one solution of green, four solutions of blue.
68,256 solutions (17,064 normalized solutions) are permutations of 948 solutions of yellow, black, and purple, 36 solutions of blue and green.
133,808 solutions (33,452 normalized solutions) are permutations of 16,726 solutions of blue, black, and purple, four solutions of yellow and green.
34,080 solutions (8,520 normalized solutions) are permutations of 426 solutions of green, black, and purple, 40 solutions of yellow and blue.
1,128 solutions (282 normalized solutions) are permutations of 188 solutions of yellow, blue, and green, one solution of black, one solution of purple.
7,520 solutions (1,880 normalized solutions) are permutations of 188 solutions of yellow, blue, and green, 20 solutions of black and purple.
4,920 solutions (1,230 normalized solutions) are permutations of 820 solutions of yellow, blue, and black, one solution of green, one solution of purple.
768 solutions (192 normalized solutions) are permutations of 32 solutions of yellow, green, and black, four solutions of blue, one solution of purple.
8,192 solutions (2,048 normalized solutions) are permutations of 32 solutions of yellow, green, and black, 128 solutions of blue and purple.
18,752 solutions (4,688 normalized solutions) are permutations of 1,172 solutions of blue, green, and black, eight solutions of yellow and purple.
31,208 solutions (7,802 normalized solutions) are permutations of 15,604 solutions of yellow, blue, green, and purple, one solution of black.
292,048 solutions (73,012 normalized solutions) are permutations of 146,024 solutions of yellow, blue, black, and purple, one solution of green.
22,304 solutions (5,576 normalized solutions) are permutations of 2,788 solutions of yellow, green, black, and purple, four solutions of blue.
14,768 solutions (3,692 normalized solutions) are permutations of 7,384 solutions of yellow, blue, green, and black, one solution of purple.
There are a total of 763,664 solutions (190,916 normalized solutions) that are permutations, leaving 1,774,228 mix solutions.
37,855 patterns are a combination of two smaller patterns.
3,555 patterns are a combination of three smaller patterns.
84 patterns are a combination of four smaller patterns.
122,234 patterns are a mix patterns.
Too many patterns to display them all.
The one suboptimal (four extra) minimal touching pattern is:

3,185 normalized solutions are not symmetric in any direction.
96 solutions (24 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, one solution of purple.
This leaves 12,644 mix solutions.
20 patterns are a combination of two smaller patterns.
1,349 patterns are a mix patterns.
Too many patterns to display them all.
The two suboptimal (seven extra) minimal touching patterns are:

49,170 normalized solutions are not symmetric in any direction.
1,760 solutions (440 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, four solutions of blue.
768 solutions (192 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, one solution of purple.
There are a total of 2,528 solutions (632 normalized solutions) that are permutations, leaving 194,152 mix solutions.
138 patterns are a combination of two smaller patterns.
14,200 patterns are a mix patterns.
Too many patterns to display them all.
The one suboptimal (three extra) minimal touching pattern is:

Two normalized solutions are symmetric in one direction.
185,696 normalized solutions are not symmetric in any direction.
1,152 solutions (288 normalized solutions) are permutations of 72 solutions of orange, blue, and white, eight solutions of yellow and purple.
5,408 solutions (1,352 normalized solutions) are permutations of 676 solutions of orange, yellow, white, and purple, four solutions of blue.
3,784 solutions (946 normalized solutions) are permutations of 1,892 solutions of orange, yellow, blue, and white, one solution of purple.
There are a total of 10,344 solutions (2,586 normalized solutions) that are permutations, leaving 732,444 mix solutions.
819 patterns are a combination of two smaller patterns.
55,844 patterns are a mix patterns.
Too many patterns to display them all.
The two suboptimal (two extra) minimal touching patterns are:

181 normalized solutions are not symmetric in any direction.
440 solutions (110 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, one solution of green.
This leaves 284 mix solutions.
46 patterns are a combination of two smaller patterns.
30 patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with nine extra.
There are two maximal touching patterns.
The patterns are:

875 normalized solutions are not symmetric in any direction.
1,352 solutions (338 normalized solutions) are permutations of 676 solutions of orange, yellow, white, and purple, one solution of green.
This leaves 2,148 mix solutions.
180 patterns are a combination of two smaller patterns.
261 patterns are a mix patterns.
There are three minimal touching patterns, which are suboptimal with ten extra.
There is one maximal touching pattern.
The patterns are:

24,925 normalized solutions are not symmetric in any direction.
432 solutions (108 normalized solutions) are permutations of 72 solutions of orange, blue, and white, one solution of green, one solution of purple.
25,240 solutions (6,310 normalized solutions) are permutations of 12,620 solutions of orange, blue, white, and purple, one solution of green.
256 solutions (64 normalized solutions) are permutations of 32 solutions of orange, green, white, and purple, four solutions of blue.
688 solutions (172 normalized solutions) are permutations of 344 solutions of orange, blue, green, and white, one solution of purple.
There are a total of 26,616 solutions (6,654 normalized solutions) that are permutations, leaving 73,084 mix solutions.
2,278 patterns are a combination of two smaller patterns.
60 patterns are a combination of three smaller patterns.
5,342 patterns are a mix patterns.
Too many patterns to display them all.
The four suboptimal (three extra) minimal touching patterns are:

Two normalized solutions are symmetric in one direction.
2,542 normalized solutions are not symmetric in any direction.
440 solutions (110 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, one solution of black.
128 solutions (32 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, one solution of purple.
There are a total of 568 solutions (142 normalized solutions) that are permutations, leaving 9,604 mix solutions.
57 patterns are a combination of two smaller patterns.
1,029 patterns are a mix patterns.
Too many patterns to display them all.
The one suboptimal (six extra) minimal touching pattern is:

Two normalized solutions are symmetric in one direction.
11,464 normalized solutions are not symmetric in any direction.
1,352 solutions (338 normalized solutions) are permutations of 676 solutions of orange, yellow, white, and purple, one solution of black.
272 solutions (68 normalized solutions) are permutations of 136 solutions of orange, yellow, black, and white, one solution of purple.
There are a total of 1,624 solutions (406 normalized solutions) that are permutations, leaving 44,236 mix solutions.
224 patterns are a combination of two smaller patterns.
5,064 patterns are a mix patterns.
Too many patterns to display them all.
The one suboptimal (three extra) minimal touching pattern is:

193,668 normalized solutions are not symmetric in any direction.
432 solutions (108 normalized solutions) are permutations of 72 solutions of orange, blue, and white, one solution of black, one solution of purple.
2,880 solutions (720 normalized solutions) are permutations of 72 solutions of orange, blue, and white, 20 solutions of black and purple.
25,240 solutions (6,310 normalized solutions) are permutations of 12,620 solutions of orange, blue, white, and purple, one solution of black.
3,776 solutions (944 normalized solutions) are permutations of 472 solutions of orange, black, white, and purple, four solutions of blue.
4,976 solutions (1,244 normalized solutions) are permutations of 2,488 solutions of orange, blue, black, and white, one solution of purple.
There are a total of 37,304 solutions (9,326 normalized solutions) that are permutations, leaving 737,368 mix solutions.
2,985 patterns are a combination of two smaller patterns.
60 patterns are a combination of three smaller patterns.
56,556 patterns are a mix patterns.
Too many patterns to display them all.
The eight optimal minimal touching patterns are:

Four normalized solutions are symmetric in one direction.
824 normalized solutions are not symmetric in any direction.
64 solutions (16 normalized solutions) are permutations of 32 solutions of orange, green, white, and purple, one solution of black.
944 solutions (236 normalized solutions) are permutations of 472 solutions of orange, black, white, and purple, one solution of green.
There are a total of 1,008 solutions (252 normalized solutions) that are permutations, leaving 2,296 mix solutions.
140 patterns are a combination of two smaller patterns.
298 patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with four extra.
There is one maximal touching pattern.
The patterns are:

## Chinese Wooden Puzzles in 10 by 8

7,826 normalized solutions are not symmetric in any direction.
384 solutions (96 normalized solutions) are permutations of 64 solutions of red, yellow, and blue, one solution of black, one solution of green.
1,280 solutions (320 normalized solutions) are permutations of 64 solutions of red, yellow, and blue, ten solutions of green and black.
352 solutions (88 normalized solutions) are permutations of 44 solutions of red, blue, and black, four solutions of yellow and green.
560 solutions (140 normalized solutions) are permutations of 280 solutions of red, yellow, blue, and green, one solution of black.
12,048 solutions (3,012 normalized solutions) are permutations of 6,024 solutions of red, yellow, blue, and black, one solution of green.
There are a total of 14,624 solutions (3,656 normalized solutions) that are permutations, leaving 16,680 mix solutions.
2,063 patterns are a combination of two smaller patterns.
54 patterns are a combination of three smaller patterns.
2,378 patterns are a mix patterns.
Too many patterns to display them all.
The 11 suboptimal (nine extra) minimal touching patterns are:

Two normalized solutions are symmetric in one direction.
10,739 normalized solutions are not symmetric in any direction.
384 solutions (96 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, four solutions of blue.
This leaves 42,576 mix solutions.
20 patterns are a combination of two smaller patterns.
4,498 patterns are a mix patterns.
Too many patterns to display them all.
The one suboptimal (seven extra) minimal touching pattern is:

43 normalized solutions are not symmetric in any direction.
96 solutions (24 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, one solution of green.
This leaves 76 mix solutions.
20 patterns are a combination of two smaller patterns.
13 patterns are a mix patterns.
There are four minimal touching patterns, which are suboptimal with 17 extra.
There is one maximal touching pattern.
The patterns are:

710 normalized solutions are not symmetric in any direction.
768 solutions (192 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, one solution of green.
This leaves 2,072 mix solutions.
92 patterns are a combination of two smaller patterns.
210 patterns are a mix patterns.
There are three minimal touching patterns, which are suboptimal with 12 extra.
There is one maximal touching pattern.
The patterns are:

Two normalized solutions are symmetric in one direction.
2,798 normalized solutions are not symmetric in any direction.
576 solutions (144 normalized solutions) are permutations of 72 solutions of orange, blue, and white, four solutions of yellow and green.
3,784 solutions (946 normalized solutions) are permutations of 1,892 solutions of orange, yellow, blue, and white, one solution of green.
There are a total of 4,360 solutions (1,090 normalized solutions) that are permutations, leaving 6,836 mix solutions.
559 patterns are a combination of two smaller patterns.
833 patterns are a mix patterns.
Too many patterns to display them all.
The three suboptimal (ten extra) minimal touching patterns are:

690 normalized solutions are not symmetric in any direction.
96 solutions (24 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, one solution of black.
This leaves 2,664 mix solutions.
20 patterns are a combination of two smaller patterns.
365 patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with 11 extra.
There are three maximal touching patterns.
The patterns are:

Three normalized solutions are symmetric in one direction.
7,058 normalized solutions are not symmetric in any direction.
768 solutions (192 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, one solution of black.
512 solutions (128 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, four solutions of blue.
There are a total of 1,280 solutions (320 normalized solutions) that are permutations, leaving 26,958 mix solutions.
103 patterns are a combination of two smaller patterns.
2,624 patterns are a mix patterns.
Too many patterns to display them all.
The one suboptimal (six extra) minimal touching pattern is:

Two normalized solutions are symmetric in one direction.
30,612 normalized solutions are not symmetric in any direction.
1,152 solutions (288 normalized solutions) are permutations of 72 solutions of orange, blue, and white, eight solutions of yellow and black.
3,784 solutions (946 normalized solutions) are permutations of 1,892 solutions of orange, yellow, blue, and white, one solution of black.
1,088 solutions (272 normalized solutions) are permutations of 136 solutions of orange, yellow, black, and white, four solutions of blue.
There are a total of 6,024 solutions (1,506 normalized solutions) that are permutations, leaving 116,428 mix solutions.
603 patterns are a combination of two smaller patterns.
12,501 patterns are a mix patterns.
Too many patterns to display them all.
The one suboptimal (six extra) minimal touching pattern is:

52 normalized solutions are not symmetric in any direction.
128 solutions (32 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, one solution of green.
This leaves 80 mix solutions.
11 patterns are a combination of two smaller patterns.
Ten patterns are a mix patterns.
There are five minimal touching patterns, which are suboptimal with 15 extra.
There are two maximal touching patterns.
The patterns are:

155 normalized solutions are not symmetric in any direction.
272 solutions (68 normalized solutions) are permutations of 136 solutions of orange, yellow, black, and white, one solution of green.
This leaves 348 mix solutions.
44 patterns are a combination of two smaller patterns.
61 patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with 13 extra.
There is one maximal touching pattern.
The patterns are:

4,796 normalized solutions are not symmetric in any direction.
432 solutions (108 normalized solutions) are permutations of 72 solutions of orange, blue, and white, one solution of black, one solution of green.
1,440 solutions (360 normalized solutions) are permutations of 72 solutions of orange, blue, and white, ten solutions of green and black.
688 solutions (172 normalized solutions) are permutations of 344 solutions of orange, blue, green, and white, one solution of black.
4,976 solutions (1,244 normalized solutions) are permutations of 2,488 solutions of orange, blue, black, and white, one solution of green.
There are a total of 7,536 solutions (1,884 normalized solutions) that are permutations, leaving 11,648 mix solutions.
847 patterns are a combination of two smaller patterns.
60 patterns are a combination of three smaller patterns.
1,420 patterns are a mix patterns.
Too many patterns to display them all.
The one suboptimal (six extra) minimal touching pattern is:

## Chinese Wooden Puzzles in 11 by 8

Seven normalized solutions are symmetric in one direction.
4,147,666 normalized solutions are not symmetric in any direction.
7,680 solutions (1,920 normalized solutions) are permutations of 64 solutions of red, yellow, and blue, 20 solutions of black and purple, one solution of green.
3,840 solutions (960 normalized solutions) are permutations of 64 solutions of red, yellow, and blue, ten solutions of green and black, one solution of purple.
54,528 solutions (13,632 normalized solutions) are permutations of 64 solutions of red, yellow, and blue, 426 solutions of green, black, and purple.
2,112 solutions (528 normalized solutions) are permutations of 44 solutions of red, blue, and black, eight solutions of yellow and purple, one solution of green.
1,056 solutions (264 normalized solutions) are permutations of 44 solutions of red, blue, and black, four solutions of yellow and green, one solution of purple.
352 solutions (88 normalized solutions) are permutations of 44 solutions of red, blue, and black, four solutions of yellow, green, and purple.
8,192 solutions (2,048 normalized solutions) are permutations of 32 solutions of yellow, green, and black, 128 solutions of red, blue, and purple.
56,256 solutions (14,064 normalized solutions) are permutations of 1,172 solutions of blue, green, and black, 24 solutions of red, yellow, and purple.
259,080 solutions (64,770 normalized solutions) are permutations of 43,180 solutions of red, yellow, blue, and purple, one solution of black, one solution of green.
863,600 solutions (215,900 normalized solutions) are permutations of 43,180 solutions of red, yellow, blue, and purple, ten solutions of green and black.
960 solutions (240 normalized solutions) are permutations of 40 solutions of red, yellow, green, and purple, one solution of black, four solutions of blue.
7,840 solutions (1,960 normalized solutions) are permutations of 40 solutions of red, yellow, green, and purple, 98 solutions of blue and black.
18,624 solutions (4,656 normalized solutions) are permutations of 1,164 solutions of red, blue, green, and purple, eight solutions of yellow and black.
21,840 solutions (5,460 normalized solutions) are permutations of 910 solutions of red, yellow, black, and purple, one solution of green, four solutions of blue.
65,520 solutions (16,380 normalized solutions) are permutations of 910 solutions of red, yellow, black, and purple, 36 solutions of blue and green.
89,600 solutions (22,400 normalized solutions) are permutations of 11,200 solutions of red, blue, black, and purple, four solutions of yellow and green.
1,680 solutions (420 normalized solutions) are permutations of 280 solutions of red, yellow, blue, and green, one solution of black, one solution of purple.
11,200 solutions (2,800 normalized solutions) are permutations of 280 solutions of red, yellow, blue, and green, 20 solutions of black and purple.
36,144 solutions (9,036 normalized solutions) are permutations of 6,024 solutions of red, yellow, blue, and black, one solution of green, one solution of purple.
10,112 solutions (2,528 normalized solutions) are permutations of 632 solutions of red, blue, green, and black, eight solutions of yellow and purple.
310,672 solutions (77,668 normalized solutions) are permutations of 155,336 solutions of red, yellow, blue, green, and purple, one solution of black.
4,438,440 solutions (1,109,610 normalized solutions) are permutations of 2,219,220 solutions of red, yellow, blue, black, and purple, one solution of green.
89,056 solutions (22,264 normalized solutions) are permutations of 11,132 solutions of red, yellow, green, black, and purple, four solutions of blue.
33,360 solutions (8,340 normalized solutions) are permutations of 16,680 solutions of red, yellow, blue, green, and black, one solution of purple.
There are a total of 6,391,744 solutions (1,597,936 normalized solutions) that are permutations, leaving 10,198,934 mix solutions.
503,512 patterns are a combination of two smaller patterns.
34,329 patterns are a combination of three smaller patterns.
336 patterns are a combination of four smaller patterns.
818,318 patterns are a mix patterns.
Too many patterns to display them all.
The four suboptimal (five extra) minimal touching patterns are:

3,456 solutions (864 normalized solutions) are permutations of 72 solutions of orange, blue, and white, 24 solutions of red, yellow, and purple.
17,600 solutions (4,400 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, 40 solutions of yellow and blue.
1,152 solutions (288 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, four solutions of blue, one solution of purple.
12,288 solutions (3,072 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 128 solutions of blue and purple.
6,144 solutions (1,536 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, eight solutions of yellow and purple.
101,152 solutions (25,288 normalized solutions) are permutations of 12,644 solutions of orange, red, yellow, white, and purple, four solutions of blue.
85,152 solutions (21,288 normalized solutions) are permutations of 42,576 solutions of orange, red, yellow, blue, and white, one solution of purple.
Which means it has at least 226,944 solutions (56,736 normalized solutions).
There exists at least minimal touching patterns with seven extra.
There are at least two such suboptimal minimal touching patterns.
One such pattern is:

1,760 solutions (440 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, four solutions of yellow and green.
288 solutions (72 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, one solution of green, one solution of purple.
25,288 solutions (6,322 normalized solutions) are permutations of 12,644 solutions of orange, red, yellow, white, and purple, one solution of green.
152 solutions (38 normalized solutions) are permutations of 76 solutions of orange, red, yellow, green, and white, one solution of purple.
Which means it has at least 27,488 solutions (6,872 normalized solutions).
There exists at least minimal touching patterns with ten extra.
There are at least four such suboptimal minimal touching patterns.
Two such patterns are:

5,280 solutions (1,320 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, one solution of green, four solutions of blue.
15,840 solutions (3,960 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, 36 solutions of blue and green.
2,304 solutions (576 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, one solution of green, one solution of purple.
388,304 solutions (97,076 normalized solutions) are permutations of 194,152 solutions of orange, red, blue, white, and purple, one solution of green.
2,272 solutions (568 normalized solutions) are permutations of 284 solutions of orange, red, green, white, and purple, four solutions of blue.
4,144 solutions (1,036 normalized solutions) are permutations of 2,072 solutions of orange, red, blue, green, and white, one solution of purple.
Which means it has at least 418,144 solutions (104,536 normalized solutions).
There exists at least minimal touching patterns with six extra.
There are at least two such suboptimal minimal touching patterns.
One such pattern is:

3,456 solutions (864 normalized solutions) are permutations of 72 solutions of orange, blue, and white, eight solutions of yellow and purple, one solution of green.
1,728 solutions (432 normalized solutions) are permutations of 72 solutions of orange, blue, and white, four solutions of yellow and green, one solution of purple.
576 solutions (144 normalized solutions) are permutations of 72 solutions of orange, blue, and white, four solutions of yellow, green, and purple.
16,224 solutions (4,056 normalized solutions) are permutations of 676 solutions of orange, yellow, white, and purple, one solution of green, four solutions of blue.
48,672 solutions (12,168 normalized solutions) are permutations of 676 solutions of orange, yellow, white, and purple, 36 solutions of blue and green.
100,960 solutions (25,240 normalized solutions) are permutations of 12,620 solutions of orange, blue, white, and purple, four solutions of yellow and green.
2,560 solutions (640 normalized solutions) are permutations of 32 solutions of orange, green, white, and purple, 40 solutions of yellow and blue.
11,352 solutions (2,838 normalized solutions) are permutations of 1,892 solutions of orange, yellow, blue, and white, one solution of green, one solution of purple.
5,504 solutions (1,376 normalized solutions) are permutations of 344 solutions of orange, blue, green, and white, eight solutions of yellow and purple.
1,464,888 solutions (366,222 normalized solutions) are permutations of 732,444 solutions of orange, yellow, blue, white, and purple, one solution of green.
17,184 solutions (4,296 normalized solutions) are permutations of 2,148 solutions of orange, yellow, green, white, and purple, four solutions of blue.
13,672 solutions (3,418 normalized solutions) are permutations of 6,836 solutions of orange, yellow, blue, green, and white, one solution of purple.
Which means it has at least 1,686,776 solutions (421,694 normalized solutions).
There exists at least minimal touching patterns with five extra.
There are at least four such suboptimal minimal touching patterns.
Two such patterns are:

3,520 solutions (880 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, eight solutions of yellow and black.
288 solutions (72 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, one solution of black, one solution of purple.
1,920 solutions (480 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 20 solutions of black and purple.
1,024 solutions (256 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, eight solutions of yellow and purple.
25,288 solutions (6,322 normalized solutions) are permutations of 12,644 solutions of orange, red, yellow, white, and purple, one solution of black.
5,328 solutions (1,332 normalized solutions) are permutations of 2,664 solutions of orange, red, yellow, black, and white, one solution of purple.
Which means it has at least 37,368 solutions (9,342 normalized solutions).
There exists at least minimal touching patterns with 11 extra.
There are at least two such suboptimal minimal touching patterns.
One such pattern is:

5,280 solutions (1,320 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, one solution of black, four solutions of blue.
43,120 solutions (10,780 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, 98 solutions of blue and black.
2,304 solutions (576 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, one solution of black, one solution of purple.
15,360 solutions (3,840 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, 20 solutions of black and purple.
1,536 solutions (384 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, four solutions of blue, one solution of purple.
16,384 solutions (4,096 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, 128 solutions of blue and purple.
388,304 solutions (97,076 normalized solutions) are permutations of 194,152 solutions of orange, red, blue, white, and purple, one solution of black.
76,832 solutions (19,208 normalized solutions) are permutations of 9,604 solutions of orange, red, black, white, and purple, four solutions of blue.
53,916 solutions (13,479 normalized solutions) are permutations of 26,958 solutions of orange, red, blue, black, and white, one solution of purple.
Which means it has at least 603,036 solutions (150,759 normalized solutions).
There exists at least minimal touching patterns with six extra.
There are at least two such suboptimal minimal touching patterns.
One such pattern is:

3,456 solutions (864 normalized solutions) are permutations of 72 solutions of orange, blue, and white, eight solutions of yellow and purple, one solution of black.
3,456 solutions (864 normalized solutions) are permutations of 72 solutions of orange, blue, and white, eight solutions of yellow and black, one solution of purple.
136,512 solutions (34,128 normalized solutions) are permutations of 72 solutions of orange, blue, and white, 948 solutions of yellow, black, and purple.
16,224 solutions (4,056 normalized solutions) are permutations of 676 solutions of orange, yellow, white, and purple, one solution of black, four solutions of blue.
132,496 solutions (33,124 normalized solutions) are permutations of 676 solutions of orange, yellow, white, and purple, 98 solutions of blue and black.
201,920 solutions (50,480 normalized solutions) are permutations of 12,620 solutions of orange, blue, white, and purple, eight solutions of yellow and black.
37,760 solutions (9,440 normalized solutions) are permutations of 472 solutions of orange, black, white, and purple, 40 solutions of yellow and blue.
11,352 solutions (2,838 normalized solutions) are permutations of 1,892 solutions of orange, yellow, blue, and white, one solution of black, one solution of purple.
75,680 solutions (18,920 normalized solutions) are permutations of 1,892 solutions of orange, yellow, blue, and white, 20 solutions of black and purple.
3,264 solutions (816 normalized solutions) are permutations of 136 solutions of orange, yellow, black, and white, four solutions of blue, one solution of purple.
34,816 solutions (8,704 normalized solutions) are permutations of 136 solutions of orange, yellow, black, and white, 128 solutions of blue and purple.
39,808 solutions (9,952 normalized solutions) are permutations of 2,488 solutions of orange, blue, black, and white, eight solutions of yellow and purple.
1,464,888 solutions (366,222 normalized solutions) are permutations of 732,444 solutions of orange, yellow, blue, white, and purple, one solution of black.
353,888 solutions (88,472 normalized solutions) are permutations of 44,236 solutions of orange, yellow, black, white, and purple, four solutions of blue.
232,856 solutions (58,214 normalized solutions) are permutations of 116,428 solutions of orange, yellow, blue, black, and white, one solution of purple.
Which means it has at least 2,748,376 solutions (687,094 normalized solutions).
There exists at least minimal touching patterns with six extra.
There are at least two such suboptimal minimal touching patterns.
One such pattern is:

1,320 solutions (330 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, one solution of black, one solution of green.
4,400 solutions (1,100 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, ten solutions of green and black.
384 solutions (96 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, one solution of green, one solution of purple.
568 solutions (142 normalized solutions) are permutations of 284 solutions of orange, red, green, white, and purple, one solution of black.
19,208 solutions (4,802 normalized solutions) are permutations of 9,604 solutions of orange, red, black, white, and purple, one solution of green.
160 solutions (40 normalized solutions) are permutations of 80 solutions of orange, red, green, black, and white, one solution of purple.
Which means it has at least 26,040 solutions (6,510 normalized solutions).
There exists at least minimal touching patterns with nine extra.
There are at least two such suboptimal minimal touching patterns.
One such pattern is:

4,056 solutions (1,014 normalized solutions) are permutations of 676 solutions of orange, yellow, white, and purple, one solution of black, one solution of green.
13,520 solutions (3,380 normalized solutions) are permutations of 676 solutions of orange, yellow, white, and purple, ten solutions of green and black.
512 solutions (128 normalized solutions) are permutations of 32 solutions of orange, green, white, and purple, eight solutions of yellow and black.
3,776 solutions (944 normalized solutions) are permutations of 472 solutions of orange, black, white, and purple, four solutions of yellow and green.
816 solutions (204 normalized solutions) are permutations of 136 solutions of orange, yellow, black, and white, one solution of green, one solution of purple.
4,296 solutions (1,074 normalized solutions) are permutations of 2,148 solutions of orange, yellow, green, white, and purple, one solution of black.
88,472 solutions (22,118 normalized solutions) are permutations of 44,236 solutions of orange, yellow, black, white, and purple, one solution of green.
696 solutions (174 normalized solutions) are permutations of 348 solutions of orange, yellow, green, black, and white, one solution of purple.
Which means it has at least 116,144 solutions (29,036 normalized solutions).
There exists at least minimal touching patterns with six extra.
There are at least two such suboptimal minimal touching patterns.
One such pattern is:

8,640 solutions (2,160 normalized solutions) are permutations of 72 solutions of orange, blue, and white, 20 solutions of black and purple, one solution of green.
4,320 solutions (1,080 normalized solutions) are permutations of 72 solutions of orange, blue, and white, ten solutions of green and black, one solution of purple.
61,344 solutions (15,336 normalized solutions) are permutations of 72 solutions of orange, blue, and white, 426 solutions of green, black, and purple.
75,720 solutions (18,930 normalized solutions) are permutations of 12,620 solutions of orange, blue, white, and purple, one solution of black, one solution of green.
252,400 solutions (63,100 normalized solutions) are permutations of 12,620 solutions of orange, blue, white, and purple, ten solutions of green and black.
768 solutions (192 normalized solutions) are permutations of 32 solutions of orange, green, white, and purple, one solution of black, four solutions of blue.
6,272 solutions (1,568 normalized solutions) are permutations of 32 solutions of orange, green, white, and purple, 98 solutions of blue and black.
11,328 solutions (2,832 normalized solutions) are permutations of 472 solutions of orange, black, white, and purple, one solution of green, four solutions of blue.
33,984 solutions (8,496 normalized solutions) are permutations of 472 solutions of orange, black, white, and purple, 36 solutions of blue and green.
2,064 solutions (516 normalized solutions) are permutations of 344 solutions of orange, blue, green, and white, one solution of black, one solution of purple.
13,760 solutions (3,440 normalized solutions) are permutations of 344 solutions of orange, blue, green, and white, 20 solutions of black and purple.
14,928 solutions (3,732 normalized solutions) are permutations of 2,488 solutions of orange, blue, black, and white, one solution of green, one solution of purple.
146,168 solutions (36,542 normalized solutions) are permutations of 73,084 solutions of orange, blue, green, white, and purple, one solution of black.
1,474,736 solutions (368,684 normalized solutions) are permutations of 737,368 solutions of orange, blue, black, white, and purple, one solution of green.
18,368 solutions (4,592 normalized solutions) are permutations of 2,296 solutions of orange, green, black, white, and purple, four solutions of blue.
23,296 solutions (5,824 normalized solutions) are permutations of 11,648 solutions of orange, blue, green, black, and white, one solution of purple.
Which means it has at least 2,148,096 solutions (537,024 normalized solutions).
There exists at least minimal touching patterns with three extra.
There are at least 16 such suboptimal minimal touching patterns.
Eight such patterns are:

## Chinese Wooden Puzzles in 12 by 8

1,152 solutions (288 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, one solution of green, four solutions of blue.
3,456 solutions (864 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 36 solutions of blue and green.
3,072 solutions (768 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, four solutions of yellow and green.
85,152 solutions (21,288 normalized solutions) are permutations of 42,576 solutions of orange, red, yellow, blue, and white, one solution of green.
608 solutions (152 normalized solutions) are permutations of 76 solutions of orange, red, yellow, green, and white, four solutions of blue.
Which means it has at least 93,440 solutions (23,360 normalized solutions).
There exists at least minimal touching patterns with ten extra.
There are at least two such suboptimal minimal touching patterns.
One such pattern is:

1,152 solutions (288 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, one solution of black, four solutions of blue.
9,408 solutions (2,352 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 98 solutions of blue and black.
6,144 solutions (1,536 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, eight solutions of yellow and black.
5,120 solutions (1,280 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, 40 solutions of yellow and blue.
85,152 solutions (21,288 normalized solutions) are permutations of 42,576 solutions of orange, red, yellow, blue, and white, one solution of black.
21,312 solutions (5,328 normalized solutions) are permutations of 2,664 solutions of orange, red, yellow, black, and white, four solutions of blue.
Which means it has at least 128,288 solutions (32,072 normalized solutions).
There exists at least minimal touching patterns with 14 extra.
There are at least two such suboptimal minimal touching patterns.
One such pattern is:

288 solutions (72 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, one solution of black, one solution of green.
960 solutions (240 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, ten solutions of green and black.
512 solutions (128 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, four solutions of yellow and green.
152 solutions (38 normalized solutions) are permutations of 76 solutions of orange, red, yellow, green, and white, one solution of black.
5,328 solutions (1,332 normalized solutions) are permutations of 2,664 solutions of orange, red, yellow, black, and white, one solution of green.
Which means it has at least 7,240 solutions (1,810 normalized solutions).
There exists at least minimal touching patterns with 14 extra.
There are at least two such suboptimal minimal touching patterns.
One such pattern is:

2,304 solutions (576 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, one solution of black, one solution of green.
7,680 solutions (1,920 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, ten solutions of green and black.
1,536 solutions (384 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, one solution of green, four solutions of blue.
4,608 solutions (1,152 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, 36 solutions of blue and green.
4,144 solutions (1,036 normalized solutions) are permutations of 2,072 solutions of orange, red, blue, green, and white, one solution of black.
53,916 solutions (13,479 normalized solutions) are permutations of 26,958 solutions of orange, red, blue, black, and white, one solution of green.
640 solutions (160 normalized solutions) are permutations of 80 solutions of orange, red, green, black, and white, four solutions of blue.
Which means it has at least 74,828 solutions (18,707 normalized solutions).
There exists at least minimal touching patterns with nine extra.
There are at least two such suboptimal minimal touching patterns.
One such pattern is:

1,728 solutions (432 normalized solutions) are permutations of 72 solutions of orange, blue, and white, four solutions of yellow and green, one solution of black.
3,456 solutions (864 normalized solutions) are permutations of 72 solutions of orange, blue, and white, eight solutions of yellow and black, one solution of green.
4,608 solutions (1,152 normalized solutions) are permutations of 72 solutions of orange, blue, and white, 32 solutions of yellow, green, and black.
11,352 solutions (2,838 normalized solutions) are permutations of 1,892 solutions of orange, yellow, blue, and white, one solution of black, one solution of green.
37,840 solutions (9,460 normalized solutions) are permutations of 1,892 solutions of orange, yellow, blue, and white, ten solutions of green and black.
5,504 solutions (1,376 normalized solutions) are permutations of 344 solutions of orange, blue, green, and white, eight solutions of yellow and black.
3,264 solutions (816 normalized solutions) are permutations of 136 solutions of orange, yellow, black, and white, one solution of green, four solutions of blue.
9,792 solutions (2,448 normalized solutions) are permutations of 136 solutions of orange, yellow, black, and white, 36 solutions of blue and green.
19,904 solutions (4,976 normalized solutions) are permutations of 2,488 solutions of orange, blue, black, and white, four solutions of yellow and green.
13,672 solutions (3,418 normalized solutions) are permutations of 6,836 solutions of orange, yellow, blue, green, and white, one solution of black.
232,856 solutions (58,214 normalized solutions) are permutations of 116,428 solutions of orange, yellow, blue, black, and white, one solution of green.
2,784 solutions (696 normalized solutions) are permutations of 348 solutions of orange, yellow, green, black, and white, four solutions of blue.
Which means it has at least 346,760 solutions (86,690 normalized solutions).
There exists at least minimal touching patterns with nine extra.
There are at least two such suboptimal minimal touching patterns.
One such pattern is:

## Chinese Wooden Puzzles in 13 by 8

5,760 solutions (1,440 normalized solutions) are permutations of 40 solutions of red, yellow, green, and purple, 72 solutions of orange, blue, and white.
52,800 solutions (13,200 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, 40 solutions of yellow and blue, one solution of green.
21,120 solutions (5,280 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, four solutions of yellow and green, four solutions of blue.
82,720 solutions (20,680 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, 188 solutions of yellow, blue, and green.
4,096 solutions (1,024 normalized solutions) are permutations of 32 solutions of orange, green, white, and purple, 64 solutions of red, yellow, and blue.
36,864 solutions (9,216 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 128 solutions of blue and purple, one solution of green.
10,368 solutions (2,592 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 36 solutions of blue and green, one solution of purple.
101,376 solutions (25,344 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 1,056 solutions of blue, green, and purple.
18,432 solutions (4,608 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, eight solutions of yellow and purple, one solution of green.
9,216 solutions (2,304 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, four solutions of yellow and green, one solution of purple.
3,072 solutions (768 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, four solutions of yellow, green, and purple.
16,512 solutions (4,128 normalized solutions) are permutations of 344 solutions of orange, blue, green, and white, 24 solutions of red, yellow, and purple.
303,456 solutions (75,864 normalized solutions) are permutations of 12,644 solutions of orange, red, yellow, white, and purple, one solution of green, four solutions of blue.
910,368 solutions (227,592 normalized solutions) are permutations of 12,644 solutions of orange, red, yellow, white, and purple, 36 solutions of blue and green.
1,553,216 solutions (388,304 normalized solutions) are permutations of 194,152 solutions of orange, red, blue, white, and purple, four solutions of yellow and green.
22,720 solutions (5,680 normalized solutions) are permutations of 284 solutions of orange, red, green, white, and purple, 40 solutions of yellow and blue.
255,456 solutions (63,864 normalized solutions) are permutations of 42,576 solutions of orange, red, yellow, blue, and white, one solution of green, one solution of purple.
1,824 solutions (456 normalized solutions) are permutations of 76 solutions of orange, red, yellow, green, and white, four solutions of blue, one solution of purple.
19,456 solutions (4,864 normalized solutions) are permutations of 76 solutions of orange, red, yellow, green, and white, 128 solutions of blue and purple.
33,152 solutions (8,288 normalized solutions) are permutations of 2,072 solutions of orange, red, blue, green, and white, eight solutions of yellow and purple.
Which means it has at least 3,461,984 solutions (865,496 normalized solutions).
There exists at least minimal touching patterns with ten extra.
There are at least six such suboptimal minimal touching patterns.
One such pattern is:

131,040 solutions (32,760 normalized solutions) are permutations of 910 solutions of red, yellow, black, and purple, 72 solutions of orange, blue, and white.
52,800 solutions (13,200 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, 40 solutions of yellow and blue, one solution of black.
42,240 solutions (10,560 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, eight solutions of yellow and black, four solutions of blue.
360,800 solutions (90,200 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, 820 solutions of yellow, blue, and black.
59,488 solutions (14,872 normalized solutions) are permutations of 676 solutions of orange, yellow, white, and purple, 44 solutions of red, blue, and black.
60,416 solutions (15,104 normalized solutions) are permutations of 472 solutions of orange, black, white, and purple, 64 solutions of red, yellow, and blue.
36,864 solutions (9,216 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 128 solutions of blue and purple, one solution of black.
23,040 solutions (5,760 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 20 solutions of black and purple, four solutions of blue.
28,224 solutions (7,056 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 98 solutions of blue and black, one solution of purple.
1,605,696 solutions (401,424 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 16,726 solutions of blue, black, and purple.
18,432 solutions (4,608 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, eight solutions of yellow and purple, one solution of black.
18,432 solutions (4,608 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, eight solutions of yellow and black, one solution of purple.
728,064 solutions (182,016 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, 948 solutions of yellow, black, and purple.
12,288 solutions (3,072 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, eight solutions of yellow and purple, four solutions of blue.
15,360 solutions (3,840 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, 40 solutions of yellow and blue, one solution of purple.
420,352 solutions (105,088 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, 3,284 solutions of yellow, blue, and purple.
34,816 solutions (8,704 normalized solutions) are permutations of 136 solutions of orange, yellow, black, and white, 128 solutions of red, blue, and purple.
119,424 solutions (29,856 normalized solutions) are permutations of 2,488 solutions of orange, blue, black, and white, 24 solutions of red, yellow, and purple.
303,456 solutions (75,864 normalized solutions) are permutations of 12,644 solutions of orange, red, yellow, white, and purple, one solution of black, four solutions of blue.
2,478,224 solutions (619,556 normalized solutions) are permutations of 12,644 solutions of orange, red, yellow, white, and purple, 98 solutions of blue and black.
3,106,432 solutions (776,608 normalized solutions) are permutations of 194,152 solutions of orange, red, blue, white, and purple, eight solutions of yellow and black.
768,320 solutions (192,080 normalized solutions) are permutations of 9,604 solutions of orange, red, black, white, and purple, 40 solutions of yellow and blue.
255,456 solutions (63,864 normalized solutions) are permutations of 42,576 solutions of orange, red, yellow, blue, and white, one solution of black, one solution of purple.
1,703,040 solutions (425,760 normalized solutions) are permutations of 42,576 solutions of orange, red, yellow, blue, and white, 20 solutions of black and purple.
63,936 solutions (15,984 normalized solutions) are permutations of 2,664 solutions of orange, red, yellow, black, and white, four solutions of blue, one solution of purple.
681,984 solutions (170,496 normalized solutions) are permutations of 2,664 solutions of orange, red, yellow, black, and white, 128 solutions of blue and purple.
431,328 solutions (107,832 normalized solutions) are permutations of 26,958 solutions of orange, red, blue, black, and white, eight solutions of yellow and purple.
Which means it has at least 13,559,952 solutions (3,389,988 normalized solutions).
There exists at least minimal touching patterns with 11 extra.
There are at least two such suboptimal minimal touching patterns.
One such pattern is:

5,280 solutions (1,320 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, four solutions of yellow and green, one solution of black.
10,560 solutions (2,640 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, eight solutions of yellow and black, one solution of green.
14,080 solutions (3,520 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, 32 solutions of yellow, green, and black.
5,760 solutions (1,440 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 20 solutions of black and purple, one solution of green.
2,880 solutions (720 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, ten solutions of green and black, one solution of purple.
40,896 solutions (10,224 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 426 solutions of green, black, and purple.
3,072 solutions (768 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, eight solutions of yellow and purple, one solution of green.
1,536 solutions (384 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, four solutions of yellow and green, one solution of purple.
512 solutions (128 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, four solutions of yellow, green, and purple.
75,864 solutions (18,966 normalized solutions) are permutations of 12,644 solutions of orange, red, yellow, white, and purple, one solution of black, one solution of green.
252,880 solutions (63,220 normalized solutions) are permutations of 12,644 solutions of orange, red, yellow, white, and purple, ten solutions of green and black.
4,544 solutions (1,136 normalized solutions) are permutations of 284 solutions of orange, red, green, white, and purple, eight solutions of yellow and black.
76,832 solutions (19,208 normalized solutions) are permutations of 9,604 solutions of orange, red, black, white, and purple, four solutions of yellow and green.
456 solutions (114 normalized solutions) are permutations of 76 solutions of orange, red, yellow, green, and white, one solution of black, one solution of purple.
3,040 solutions (760 normalized solutions) are permutations of 76 solutions of orange, red, yellow, green, and white, 20 solutions of black and purple.
15,984 solutions (3,996 normalized solutions) are permutations of 2,664 solutions of orange, red, yellow, black, and white, one solution of green, one solution of purple.
1,280 solutions (320 normalized solutions) are permutations of 80 solutions of orange, red, green, black, and white, eight solutions of yellow and purple.
Which means it has at least 515,456 solutions (128,864 normalized solutions).
There exists at least minimal touching patterns with 13 extra.
There are at least four such suboptimal minimal touching patterns.
Two such patterns are:

47,520 solutions (11,880 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, 36 solutions of blue and green, one solution of black.
129,360 solutions (32,340 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, 98 solutions of blue and black, one solution of green.
52,800 solutions (13,200 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, ten solutions of green and black, four solutions of blue.
515,680 solutions (128,920 normalized solutions) are permutations of 220 solutions of orange, red, white, and purple, 1,172 solutions of blue, green, and black.
2,816 solutions (704 normalized solutions) are permutations of 32 solutions of orange, green, white, and purple, 44 solutions of red, blue, and black.
46,080 solutions (11,520 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, 20 solutions of black and purple, one solution of green.
23,040 solutions (5,760 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, ten solutions of green and black, one solution of purple.
327,168 solutions (81,792 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, 426 solutions of green, black, and purple.
49,152 solutions (12,288 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, 128 solutions of blue and purple, one solution of green.
13,824 solutions (3,456 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, 36 solutions of blue and green, one solution of purple.
135,168 solutions (33,792 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, 1,056 solutions of blue, green, and purple.
1,164,912 solutions (291,228 normalized solutions) are permutations of 194,152 solutions of orange, red, blue, white, and purple, one solution of black, one solution of green.
3,883,040 solutions (970,760 normalized solutions) are permutations of 194,152 solutions of orange, red, blue, white, and purple, ten solutions of green and black.
6,816 solutions (1,704 normalized solutions) are permutations of 284 solutions of orange, red, green, white, and purple, one solution of black, four solutions of blue.
55,664 solutions (13,916 normalized solutions) are permutations of 284 solutions of orange, red, green, white, and purple, 98 solutions of blue and black.
230,496 solutions (57,624 normalized solutions) are permutations of 9,604 solutions of orange, red, black, white, and purple, one solution of green, four solutions of blue.
691,488 solutions (172,872 normalized solutions) are permutations of 9,604 solutions of orange, red, black, white, and purple, 36 solutions of blue and green.
12,432 solutions (3,108 normalized solutions) are permutations of 2,072 solutions of orange, red, blue, green, and white, one solution of black, one solution of purple.
82,880 solutions (20,720 normalized solutions) are permutations of 2,072 solutions of orange, red, blue, green, and white, 20 solutions of black and purple.
161,748 solutions (40,437 normalized solutions) are permutations of 26,958 solutions of orange, red, blue, black, and white, one solution of green, one solution of purple.
1,920 solutions (480 normalized solutions) are permutations of 80 solutions of orange, red, green, black, and white, four solutions of blue, one solution of purple.
20,480 solutions (5,120 normalized solutions) are permutations of 80 solutions of orange, red, green, black, and white, 128 solutions of blue and purple.
Which means it has at least 7,654,484 solutions (1,913,621 normalized solutions).
There exists at least minimal touching patterns with nine extra.
There are at least eight such suboptimal minimal touching patterns.
Two such patterns are:

401,472 solutions (100,368 normalized solutions) are permutations of 2,788 solutions of yellow, green, black, and purple, 72 solutions of orange, blue, and white.
146,016 solutions (36,504 normalized solutions) are permutations of 676 solutions of orange, yellow, white, and purple, 36 solutions of blue and green, one solution of black.
397,488 solutions (99,372 normalized solutions) are permutations of 676 solutions of orange, yellow, white, and purple, 98 solutions of blue and black, one solution of green.
162,240 solutions (40,560 normalized solutions) are permutations of 676 solutions of orange, yellow, white, and purple, ten solutions of green and black, four solutions of blue.
1,584,544 solutions (396,136 normalized solutions) are permutations of 676 solutions of orange, yellow, white, and purple, 1,172 solutions of blue, green, and black.
302,880 solutions (75,720 normalized solutions) are permutations of 12,620 solutions of orange, blue, white, and purple, four solutions of yellow and green, one solution of black.
605,760 solutions (151,440 normalized solutions) are permutations of 12,620 solutions of orange, blue, white, and purple, eight solutions of yellow and black, one solution of green.
807,680 solutions (201,920 normalized solutions) are permutations of 12,620 solutions of orange, blue, white, and purple, 32 solutions of yellow, green, and black.
7,680 solutions (1,920 normalized solutions) are permutations of 32 solutions of orange, green, white, and purple, 40 solutions of yellow and blue, one solution of black.
6,144 solutions (1,536 normalized solutions) are permutations of 32 solutions of orange, green, white, and purple, eight solutions of yellow and black, four solutions of blue.
52,480 solutions (13,120 normalized solutions) are permutations of 32 solutions of orange, green, white, and purple, 820 solutions of yellow, blue, and black.
113,280 solutions (28,320 normalized solutions) are permutations of 472 solutions of orange, black, white, and purple, 40 solutions of yellow and blue, one solution of green.
45,312 solutions (11,328 normalized solutions) are permutations of 472 solutions of orange, black, white, and purple, four solutions of yellow and green, four solutions of blue.
177,472 solutions (44,368 normalized solutions) are permutations of 472 solutions of orange, black, white, and purple, 188 solutions of yellow, blue, and green.
227,040 solutions (56,760 normalized solutions) are permutations of 1,892 solutions of orange, yellow, blue, and white, 20 solutions of black and purple, one solution of green.
113,520 solutions (28,380 normalized solutions) are permutations of 1,892 solutions of orange, yellow, blue, and white, ten solutions of green and black, one solution of purple.
1,611,984 solutions (402,996 normalized solutions) are permutations of 1,892 solutions of orange, yellow, blue, and white, 426 solutions of green, black, and purple.
16,512 solutions (4,128 normalized solutions) are permutations of 344 solutions of orange, blue, green, and white, eight solutions of yellow and purple, one solution of black.
16,512 solutions (4,128 normalized solutions) are permutations of 344 solutions of orange, blue, green, and white, eight solutions of yellow and black, one solution of purple.
652,224 solutions (163,056 normalized solutions) are permutations of 344 solutions of orange, blue, green, and white, 948 solutions of yellow, black, and purple.
104,448 solutions (26,112 normalized solutions) are permutations of 136 solutions of orange, yellow, black, and white, 128 solutions of blue and purple, one solution of green.
29,376 solutions (7,344 normalized solutions) are permutations of 136 solutions of orange, yellow, black, and white, 36 solutions of blue and green, one solution of purple.
287,232 solutions (71,808 normalized solutions) are permutations of 136 solutions of orange, yellow, black, and white, 1,056 solutions of blue, green, and purple.
119,424 solutions (29,856 normalized solutions) are permutations of 2,488 solutions of orange, blue, black, and white, eight solutions of yellow and purple, one solution of green.
59,712 solutions (14,928 normalized solutions) are permutations of 2,488 solutions of orange, blue, black, and white, four solutions of yellow and green, one solution of purple.
19,904 solutions (4,976 normalized solutions) are permutations of 2,488 solutions of orange, blue, black, and white, four solutions of yellow, green, and purple.
4,394,664 solutions (1,098,666 normalized solutions) are permutations of 732,444 solutions of orange, yellow, blue, white, and purple, one solution of black, one solution of green.
14,648,880 solutions (3,662,220 normalized solutions) are permutations of 732,444 solutions of orange, yellow, blue, white, and purple, ten solutions of green and black.
51,552 solutions (12,888 normalized solutions) are permutations of 2,148 solutions of orange, yellow, green, white, and purple, one solution of black, four solutions of blue.
421,008 solutions (105,252 normalized solutions) are permutations of 2,148 solutions of orange, yellow, green, white, and purple, 98 solutions of blue and black.
1,169,344 solutions (292,336 normalized solutions) are permutations of 73,084 solutions of orange, blue, green, white, and purple, eight solutions of yellow and black.
1,061,664 solutions (265,416 normalized solutions) are permutations of 44,236 solutions of orange, yellow, black, white, and purple, one solution of green, four solutions of blue.
3,184,992 solutions (796,248 normalized solutions) are permutations of 44,236 solutions of orange, yellow, black, white, and purple, 36 solutions of blue and green.
5,898,944 solutions (1,474,736 normalized solutions) are permutations of 737,368 solutions of orange, blue, black, white, and purple, four solutions of yellow and green.
183,680 solutions (45,920 normalized solutions) are permutations of 2,296 solutions of orange, green, black, white, and purple, 40 solutions of yellow and blue.
41,016 solutions (10,254 normalized solutions) are permutations of 6,836 solutions of orange, yellow, blue, green, and white, one solution of black, one solution of purple.
273,440 solutions (68,360 normalized solutions) are permutations of 6,836 solutions of orange, yellow, blue, green, and white, 20 solutions of black and purple.
698,568 solutions (174,642 normalized solutions) are permutations of 116,428 solutions of orange, yellow, blue, black, and white, one solution of green, one solution of purple.
8,352 solutions (2,088 normalized solutions) are permutations of 348 solutions of orange, yellow, green, black, and white, four solutions of blue, one solution of purple.
89,088 solutions (22,272 normalized solutions) are permutations of 348 solutions of orange, yellow, green, black, and white, 128 solutions of blue and purple.
186,368 solutions (46,592 normalized solutions) are permutations of 11,648 solutions of orange, blue, green, black, and white, eight solutions of yellow and purple.
Which means it has at least 40,379,896 solutions (10,094,974 normalized solutions).
There exists at least minimal touching patterns with eight extra.
There are at least four such suboptimal minimal touching patterns.
Two such patterns are:

## Chinese Wooden Puzzles in 14 by 8

10,368 solutions (2,592 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 36 solutions of blue and green, one solution of black.
28,224 solutions (7,056 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 98 solutions of blue and black, one solution of green.
11,520 solutions (2,880 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, ten solutions of green and black, four solutions of blue.
112,512 solutions (28,128 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 1,172 solutions of blue, green, and black.
9,216 solutions (2,304 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, four solutions of yellow and green, one solution of black.
18,432 solutions (4,608 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, eight solutions of yellow and black, one solution of green.
24,576 solutions (6,144 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, 32 solutions of yellow, green, and black.
15,360 solutions (3,840 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, 40 solutions of yellow and blue, one solution of green.
6,144 solutions (1,536 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, four solutions of yellow and green, four solutions of blue.
24,064 solutions (6,016 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, 188 solutions of yellow, blue, and green.
255,456 solutions (63,864 normalized solutions) are permutations of 42,576 solutions of orange, red, yellow, blue, and white, one solution of black, one solution of green.
851,520 solutions (212,880 normalized solutions) are permutations of 42,576 solutions of orange, red, yellow, blue, and white, ten solutions of green and black.
1,824 solutions (456 normalized solutions) are permutations of 76 solutions of orange, red, yellow, green, and white, one solution of black, four solutions of blue.
14,896 solutions (3,724 normalized solutions) are permutations of 76 solutions of orange, red, yellow, green, and white, 98 solutions of blue and black.
33,152 solutions (8,288 normalized solutions) are permutations of 2,072 solutions of orange, red, blue, green, and white, eight solutions of yellow and black.
63,936 solutions (15,984 normalized solutions) are permutations of 2,664 solutions of orange, red, yellow, black, and white, one solution of green, four solutions of blue.
191,808 solutions (47,952 normalized solutions) are permutations of 2,664 solutions of orange, red, yellow, black, and white, 36 solutions of blue and green.
215,664 solutions (53,916 normalized solutions) are permutations of 26,958 solutions of orange, red, blue, black, and white, four solutions of yellow and green.
6,400 solutions (1,600 normalized solutions) are permutations of 80 solutions of orange, red, green, black, and white, 40 solutions of yellow and blue.
Which means it has at least 1,895,072 solutions (473,768 normalized solutions).
There exists at least minimal touching patterns with 13 extra.
There are at least two such suboptimal minimal touching patterns.
One such pattern is:

## Chinese Wooden Puzzles in 15 by 8

264,320 solutions (66,080 normalized solutions) are permutations of 280 solutions of red, yellow, blue, and green, 472 solutions of orange, black, white, and purple.
385,536 solutions (96,384 normalized solutions) are permutations of 6,024 solutions of red, yellow, blue, and black, 32 solutions of orange, green, white, and purple.
854,464 solutions (213,616 normalized solutions) are permutations of 632 solutions of red, blue, green, and black, 676 solutions of orange, yellow, white, and purple.
3,248,960 solutions (812,240 normalized solutions) are permutations of 7,384 solutions of yellow, blue, green, and black, 220 solutions of orange, red, white, and purple.
41,472 solutions (10,368 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 36 solutions of blue and green, one solution of black, one solution of purple.
207,360 solutions (51,840 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 36 solutions of blue and green, 20 solutions of black and purple.
112,896 solutions (28,224 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 98 solutions of blue and black, one solution of green, one solution of purple.
46,080 solutions (11,520 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, ten solutions of green and black, four solutions of blue, one solution of purple.
368,640 solutions (92,160 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, ten solutions of green and black, 128 solutions of blue and purple.
304,128 solutions (76,032 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 1,056 solutions of blue, green, and purple, one solution of black.
4,817,088 solutions (1,204,272 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 16,726 solutions of blue, black, and purple, one solution of green.
490,752 solutions (122,688 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 426 solutions of green, black, and purple, four solutions of blue.
337,536 solutions (84,384 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 1,172 solutions of blue, green, and black, one solution of purple.
10,480,512 solutions (2,620,128 normalized solutions) are permutations of 48 solutions of orange, red, yellow, and white, 109,172 solutions of blue, green, black, and purple.
36,864 solutions (9,216 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, four solutions of yellow and green, one solution of black, one solution of purple.
184,320 solutions (46,080 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, four solutions of yellow and green, 20 solutions of black and purple.
73,728 solutions (18,432 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, eight solutions of yellow and black, one solution of green, one solution of purple.
184,320 solutions (46,080 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, ten solutions of green and black, eight solutions of yellow and purple.
9,216 solutions (2,304 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, four solutions of yellow, green, and purple, one solution of black.
2,184,192 solutions (546,048 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, 948 solutions of yellow, black, and purple, one solution of green.
73,728 solutions (18,432 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, 32 solutions of yellow, green, and black, one solution of purple.
2,141,184 solutions (535,296 normalized solutions) are permutations of 384 solutions of orange, red, blue, and white, 2,788 solutions of yellow, green, black, and purple.
49,536 solutions (12,384 normalized solutions) are permutations of 344 solutions of orange, blue, green, and white, 24 solutions of red, yellow, and purple, one solution of black.
626,080 solutions (156,520 normalized solutions) are permutations of 344 solutions of orange, blue, green, and white, 910 solutions of red, yellow, black, and purple.
61,440 solutions (15,360 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, 40 solutions of yellow and blue, one solution of green, one solution of purple.
24,576 solutions (6,144 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, four solutions of yellow and green, four solutions of blue, one solution of purple.
196,608 solutions (49,152 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, four solutions of yellow and green, 128 solutions of blue and purple.
110,592 solutions (27,648 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, 36 solutions of blue and green, eight solutions of yellow and purple.
1,261,056 solutions (315,264 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, 3,284 solutions of yellow, blue, and purple, one solution of green.
6,144 solutions (1,536 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, four solutions of yellow, green, and purple, four solutions of blue.
72,192 solutions (18,048 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, 188 solutions of yellow, blue, and green, one solution of purple.
1,997,312 solutions (499,328 normalized solutions) are permutations of 64 solutions of orange, red, black, and white, 15,604 solutions of yellow, blue, green, and purple.
104,448 solutions (26,112 normalized solutions) are permutations of 136 solutions of orange, yellow, black, and white, 128 solutions of red, blue, and purple, one solution of green.
316,608 solutions (79,152 normalized solutions) are permutations of 136 solutions of orange, yellow, black, and white, 1,164 solutions of red, blue, green, and purple.
358,272 solutions (89,568 normalized solutions) are permutations of 2,488 solutions of orange, blue, black, and white, 24 solutions of red, yellow, and purple, one solution of green.
199,040 solutions (49,760 normalized solutions) are permutations of 2,488 solutions of orange, blue, black, and white, 40 solutions of red, yellow, green, and purple.
1,603,008 solutions (400,752 normalized solutions) are permutations of 11,132 solutions of red, yellow, green, black, and purple, 72 solutions of orange, blue, and white.
2,731,104 solutions (682,776 normalized solutions) are permutations of 12,644 solutions of orange, red, yellow, white, and purple, 36 solutions of blue and green, one solution of black.
7,434,672 solutions (1,858,668 normalized solutions) are permutations of 12,644 solutions of orange, red, yellow, white, and purple, 98 solutions of blue and black, one solution of green.
3,034,560 solutions (758,640 normalized solutions) are permutations of 12,644 solutions of orange, red, yellow, white, and purple, ten solutions of green and black, four solutions of blue.
29,637,536 solutions (7,409,384 normalized solutions) are permutations of 12,644 solutions of orange, red, yellow, white, and purple, 1,172 solutions of blue, green, and black.
4,659,648 solutions (1,164,912 normalized solutions) are permutations of 194,152 solutions of orange, red, blue, white, and purple, four solutions of yellow and green, one solution of black.
9,319,296 solutions (2,329,824 normalized solutions) are permutations of 194,152 solutions of orange, red, blue, white, and purple, eight solutions of yellow and black, one solution of green.
12,425,728 solutions (3,106,432 normalized solutions) are permutations of 194,152 solutions of orange, red, blue, white, and purple, 32 solutions of yellow, green, and black.
68,160 solutions (17,040 normalized solutions) are permutations of 284 solutions of orange, red, green, white, and purple, 40 solutions of yellow and blue, one solution of black.
54,528 solutions (13,632 normalized solutions) are permutations of 284 solutions of orange, red, green, white, and purple, eight solutions of yellow and black, four solutions of blue.
465,760 solutions (116,440 normalized solutions) are permutations of 284 solutions of orange, red, green, white, and purple, 820 solutions of yellow, blue, and black.
189,024 solutions (47,256 normalized solutions) are permutations of 2,148 solutions of orange, yellow, green, white, and purple, 44 solutions of red, blue, and black.
2,304,960 solutions (576,240 normalized solutions) are permutations of 9,604 solutions of orange, red, black, white, and purple, 40 solutions of yellow and blue, one solution of green.
921,984 solutions (230,496 normalized solutions) are permutations of 9,604 solutions of orange, red, black, white, and purple, four solutions of yellow and green, four solutions of blue.
3,611,104 solutions (902,776 normalized solutions) are permutations of 9,604 solutions of orange, red, black, white, and purple, 188 solutions of yellow, blue, and green.
293,888 solutions (73,472 normalized solutions) are permutations of 2,296 solutions of orange, green, black, white, and purple, 64 solutions of red, yellow, and blue.
5,109,120 solutions (1,277,280 normalized solutions) are permutations of 42,576 solutions of orange, red, yellow, blue, and white, 20 solutions of black and purple, one solution of green.
2,554,560 solutions (638,640 normalized solutions) are permutations of 42,576 solutions of orange, red, yellow, blue, and white, ten solutions of green and black, one solution of purple.
36,274,752 solutions (9,068,688 normalized solutions) are permutations of 42,576 solutions of orange, red, yellow, blue, and white, 426 solutions of green, black, and purple.
58,368 solutions (14,592 normalized solutions) are permutations of 76 solutions of orange, red, yellow, green, and white, 128 solutions of blue and purple, one solution of black.
36,480 solutions (9,120 normalized solutions) are permutations of 76 solutions of orange, red, yellow, green, and white, 20 solutions of black and purple, four solutions of blue.
44,688 solutions (11,172 normalized solutions) are permutations of 76 solutions of orange, red, yellow, green, and white, 98 solutions of blue and black, one solution of purple.
2,542,352 solutions (635,588 normalized solutions) are permutations of 76 solutions of orange, red, yellow, green, and white, 16,726 solutions of blue, black, and purple.
99,456 solutions (24,864 normalized solutions) are permutations of 2,072 solutions of orange, red, blue, green, and white, eight solutions of yellow and purple, one solution of black.
99,456 solutions (24,864 normalized solutions) are permutations of 2,072 solutions of orange, red, blue, green, and white, eight solutions of yellow and black, one solution of purple.
3,928,512 solutions (982,128 normalized solutions) are permutations of 2,072 solutions of orange, red, blue, green, and white, 948 solutions of yellow, black, and purple.
2,045,952 solutions (511,488 normalized solutions) are permutations of 2,664 solutions of orange, red, yellow, black, and white, 128 solutions of blue and purple, one solution of green.
575,424 solutions (143,856 normalized solutions) are permutations of 2,664 solutions of orange, red, yellow, black, and white, 36 solutions of blue and green, one solution of purple.
5,626,368 solutions (1,406,592 normalized solutions) are permutations of 2,664 solutions of orange, red, yellow, black, and white, 1,056 solutions of blue, green, and purple.
1,293,984 solutions (323,496 normalized solutions) are permutations of 26,958 solutions of orange, red, blue, black, and white, eight solutions of yellow and purple, one solution of green.
646,992 solutions (161,748 normalized solutions) are permutations of 26,958 solutions of orange, red, blue, black, and white, four solutions of yellow and green, one solution of purple.
215,664 solutions (53,916 normalized solutions) are permutations of 26,958 solutions of orange, red, blue, black, and white, four solutions of yellow, green, and purple.
15,360 solutions (3,840 normalized solutions) are permutations of 80 solutions of orange, red, green, black, and white, eight solutions of yellow and purple, four solutions of blue.
19,200 solutions (4,800 normalized solutions) are permutations of 80 solutions of orange, red, green, black, and white, 40 solutions of yellow and blue, one solution of purple.
525,440 solutions (131,360 normalized solutions) are permutations of 80 solutions of orange, red, green, black, and white, 3,284 solutions of yellow, blue, and purple.
89,088 solutions (22,272 normalized solutions) are permutations of 348 solutions of orange, yellow, green, black, and white, 128 solutions of red, blue, and purple.
559,104 solutions (139,776 normalized solutions) are permutations of 11,648 solutions of orange, blue, green, black, and white, 24 solutions of red, yellow, and purple.
Which means it has at least 173,346,480 solutions (43,336,620 normalized solutions).
There exists at least minimal touching patterns with nine extra.
There are at least four such suboptimal minimal touching patterns.
Two such patterns are:

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