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**Wild**from 1965 by Frank Stella.**Zonder titel**from 2000/01 by Han Schuil.**The Sisters**(The Grand Family no. 7) from 1996 by Zhang Xiaogang.**Random objectivation**from 1970 by Herman de Vries.**Random objectivation**from 1972 by Herman de Vries.- Om 15:59
**Falaises près de Pourville**from 1882 by Claude Monet.

*Kort Amerikaans*by Jan Wolkers. ISBN:9020806009.*De komst van Joachim Stiller*by Hubert Lampo. ISBN:9001550169 (Nederland) of 9030931108 (België).*Alles op de fiets*by Rutger Kopland. ISBN:9001955711 of 9001493203.

For the path graphs the program tries all possibilities
for finding a solution by combining smaller solutions.
A solution can be extended by adding one at the end.
This means that Symple Number for P_{n} is at
most one more than the number for P_{n-1}.
It is also possible to combine two solutions with one
or two positions in the middle, meaning that the
Symple Number of P_{n} can be calculated
with the Symple Number of P_{n1} and
P_{n2} where *n1*+*n2*+1==*n*
or *n1*+*n2*+2==*n*. But in this case, the
number of groups in each solution should be taken into
account, because these need to be added. The remaining
number of steps can be made simultaneously. The maximum
of these should be added, and finally one to connect
the two solutions. A colleague came up with the formulea
2*sqrt(*n*) - 2 + 4log(*n*) as an approximation.
The results (as printed by the program) by number of groups,
preceded by 2*sqrt(n) - 2 + 4log(n), are:

2: 1.328427 2 3: 2.256583 3 3 4: 3.000000 4 3 5: 3.633100 5 4 5 6: 4.191461 6 4 5 7: 4.695180 7 5 5 6 8: 5.156854 8 5 5 6 9: 5.584963 9 6 6 6 8 10: 5.985519 10 6 6 6 8 11: 6.362965 11 7 6 7 8 9 12: 6.720684 12 7 7 7 8 9 13: 7.061322 13 8 7 7 8 9 10 14: 7.386992 14 8 7 7 8 9 10 15: 7.699412 15 9 8 8 8 9 10 11 16: 8.000000 16 9 8 8 8 9 10 11 17: 8.289943 17 10 8 8 9 9 10 11 13 18: 8.570244 18 10 9 8 9 9 10 11 13 19: 8.841762 19 11 9 9 9 10 10 11 13 14

Calculating the Symple Number for square grid graphs
is far more complicated, because there are far more
possibilities to split a square grid graph in two parts.
To calculate an upper limit, the program only calculates
splits along a line cutting the graph in two smaller
square grid graphs. Again the number of groups need to
be taken into account. Joining two square grid graphs
with a P_{m} graph, requires *m*
steps. Also here the trick of covering two points can
be used, if the square grid graph with the largest
number of simultaneous steps can be filled at the side.
For this reason we define S(*n*,*m*,*g*)
as an upper limit for the Symple Number of the graph
P_{n}xP_{m} that is
calculated by joining two smaller square grid graphs
with a P_{m} graph or extending a single
square grid graph with such a graph. For such a graph
it is true that either a vertex at the top or at the
bottom can be filled as a last step. Which means that
a rotated form can be used as a candidate for reduction
for a larger square grid graph. The program produces
the following table for S(*n*,*m*,*g*)
where the minimum Symple Number and the smallest number
of groups for which it occurs are given:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1: 1, 1 2, 1 3, 1 3, 2 4, 2 4, 2 5, 2 5, 2 6, 2 6, 2 6, 3 7, 2 7, 3 7, 3 8, 3 8, 3 8, 3 8, 4 9, 3 2: 2, 1 4, 1 5, 2 6, 2 7, 2 8, 2 9, 2 10, 2 11, 2 12, 2 13, 2 13, 3 14, 3 15, 3 15, 3 16, 3 16, 4 17, 3 17, 4 3: 3, 1 6, 1 7, 2 8, 3 10, 2 11, 3 12, 3 13, 3 14, 4 16, 3 17, 4 19, 3 19, 3 20, 4 20, 4 21, 5 22, 4 23, 4 23, 4 4: 3, 2 7, 2 9, 2 10, 3 12, 4 13, 5 15, 4 16, 4 17, 5 18, 5 19, 5 20, 6 21, 6 22, 6 23, 6 25, 5 26, 5 27, 6 27, 6 5: 4, 2 9, 2 11, 2 12, 3 14, 4 16, 3 17, 4 19, 4 20, 4 21, 5 22, 6 24, 6 25, 8 28, 5 29, 6 31, 4 32, 4 32, 5 33, 6 6: 4, 2 10, 2 12, 4 14, 3 16, 4 18, 5 20, 4 21, 5 23, 5 24, 5 25, 6 27, 6 28, 6 29, 8 31, 6 32,11 34, 6 36, 6 37, 6 7: 5, 2 12, 2 14, 4 16, 3 18, 4 20, 5 22, 4 24, 5 25, 6 27, 5 28, 6 29, 7 31, 6 32, 7 33, 8 35, 7 36, 8 40, 7 41, 8 8: 5, 2 13, 2 15, 4 18, 3 20, 4 22, 5 24, 6 26, 5 28, 6 29, 7 31, 8 32, 9 34, 8 35, 9 37, 8 38, 9 39,10 42, 9 43,10 9: 6, 2 15, 2 17, 4 20, 3 22, 4 24, 6 27, 4 29, 6 30, 6 32, 7 33, 8 35, 7 37, 7 38, 8 39, 8 41,10 42,10 44, 8 45, 8 10: 6, 2 16, 2 18, 4 22, 3 24, 4 27, 5 29, 6 31, 6 33, 6 34, 9 36, 8 37, 9 39, 8 41, 9 42,10 44, 9 46, 8 47,10 48,10 11: 6, 3 17, 3 20, 4 24, 3 26, 4 29, 6 31, 7 33, 6 35, 6 37, 7 38, 8 40, 9 42, 9 43,11 45, 8 47,10 48,10 50,11 51,12 12: 7, 2 19, 2 21, 4 26, 3 28, 4 32, 5 33, 8 36, 6 38, 6 40, 7 41, 8 43,10 44,11 46,13 48,10 50, 9 51,10 53,11 54,12 13: 7, 3 20, 3 23, 4 28, 3 30, 4 33, 5 35, 6 37, 8 40, 6 42, 7 43, 8 45,10 47,10 49, 9 50,10 52,12 54,10 55,12 57,10 14: 7, 3 21, 3 24, 4 30, 3 32, 4 35, 6 37, 8 40, 7 42, 8 45, 8 46,12 48,10 50, 8 51,13 53,10 55,12 56,13 58,15 60,12 15: 8, 3 23, 3 26, 4 31, 5 33, 6 36, 6 39, 8 41,10 44, 8 47, 7 49, 8 50,10 52,10 54,11 55,12 57,14 59,10 61,12 62,12 16: 8, 3 24, 3 27, 4 33, 5 35, 6 39, 5 41, 6 43, 8 46,10 49, 7 51, 8 53,10 54,11 56,13 58,14 60,16 62,12 64,14 65,12 17: 8, 3 25, 3 28, 6 34, 6 37, 6 40, 6 43, 8 46, 8 48,10 52, 7 53, 8 55,10 57,12 59,11 61,12 63,14 65,11 66,13 67,14 18: 8, 4 26, 4 30, 4 36, 5 38, 6 42, 6 45, 8 48, 9 51, 8 53, 9 55,10 58,10 60,12 63,13 65,10 66,12 67,13 69,15 70,16 19: 9, 3 28, 3 31, 6 37, 6 40, 6 44, 6 46, 8 49, 9 52, 8 55,10 58, 8 60,10 62,12 65,10 67,11 68,12 69,14 71,15 72,16

- S(16,6,11) = 32 = 5 + 6 + 15 + 6 from rotated S(6,7,5) = 20 = 5 + 15 and rotated S(6,8,6) = 22 = 6 + 16 (with one reduced) and column in the middle
- S(6,7,5) = 20 = 2 + 3 + 8 + 7 from rotated S(7,2,2) = 9 = 2 + 7 and rotated S(7,3,3) = 12 = 3 + 9 (with one reduced) and column in the middle
- S(7,2,2) = 9 = 1 + 1 + 5 + 2 from rotated S(2,3,1) = 6 = 1 + 5 and rotated S(2,3,1) = 6 = 1 + 5 and column in the middle
- S(7,3,3) = 12 = 1 + 2 + 6 + 3 from rotated S(3,2,1) = 6 = 1 + 5 and rotated S(3,4,2) = 9 = 2 + 7 (with one reduced) and column in the middle
- S(3,4,2) = 9 = 1 + 1 + 3 + 4 from rotated S(4,1,1) = 4 = 1 + 3 and rotated S(4,1,1) = 4 = 1 + 3 and column in the middle

- S(6,8,6) = 22 = 2 + 4 + 8 + 8 from rotated S(8,2,2) = 10 = 2 + 8 and rotated S(8,3,4) = 13 = 4 + 9 (with one reduced) and column in the middle
- S(8,2,2) = 10 = 1 + 1 + 6 + 2 from rotated S(2,3,1) = 6 = 1 + 5 and rotated S(2,4,1) = 8 = 1 + 7 (with one reduced) and column in the middle
- S(8,3,4) = 13 = 2 + 2 + 6 + 3 from rotated S(3,3,2) = 7 = 2 + 5 and rotated S(3,4,2) = 9 = 2 + 7 (with one reduced) and column in the middle
- S(3,3,2) = 7 = 1 + 1 + 2 + 3 from rotated S(3,1,1) = 3 = 1 + 2 and rotated S(3,1,1) = 3 = 1 + 2 and column in the middle
- S(3,4,2) = 9 = 1 + 1 + 3 + 4 from rotated S(4,1,1) = 4 = 1 + 3 and rotated S(4,1,1) = 4 = 1 + 3 and column in the middle

- S(6,7,5) = 20 = 2 + 3 + 8 + 7 from rotated S(7,2,2) = 9 = 2 + 7 and rotated S(7,3,3) = 12 = 3 + 9 (with one reduced) and column in the middle

Which could be made graphical in the following figure, where '#' is used for groups, '-' and '|' for the connecting path graphs, and '+' the points that act as a reduction point.

###|###|###|+### ###|###|###|#### -------|+------- ##+####|###+#### ##|+---|---|+--- ##|####|###|####

That this can be filled in 32 steps is shown in the following, where the steps are marked with 'a' to 'z' and 'A' to 'F':

almqblmCclmrrdlm noprnopBnopsnopq uvtwxyzAAuvtwxyz eltflmnDglmthlmn mnrropqEnoprropq opsilmnFjlmsklmn

Although, the rules of Symple are rather simple, I feel that they still could be made simpler. One of the problems when playing the game (without computer support) is that you often forget which groups you already have grown. And also the rule that if two groups grow on a shared field that it counts as if both groups have grown, is rather complicated. What would happen if all restrictions on where you can grow are removed? Simply stating that you can grow as many stones as you have groups. That means that if you want to grow in a certain move, you simply take a number of stones equal to the number groups you have. Would this game, that I would brand Super Sympe, be substantial different from Symple? And how different would it be? Whether invasions at the end of the game are possible, depends on the number of groups the opponent has. Interesting.

- 2: Bach on Trance
- 2: Jackie Evancho on The Tonight Show with Jay Leno
- 12: NELL: Never-Ending Language Learning
- 12: GoTools
- 19: Eric Fischer's photostream

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