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if ((unsigned char)(*str) < ' ')The "char" type was introduced for the representation of characters. At first only the ANSI characters raging from 0 to 128 (not including). These values fit in 7 bits, so when the byte became the default smallest unit of storage consisting of 8 bits, there were two choices to extend the range. The implementors of C decided that the "char" type would be a signed type with values ranging from -127 to 128. Although this chouce gives you a 'small' integer with negative and positive values, it also has lead to many programming errors, because it is more natural to think that it ranges from 0 to 256. The type "unsigned char" ranges from 0 to 256, where the values 128 to 256 map on -127 to 0. Appearantly, it also has lead to errors in the machine code optimizer of Visual Studio 2008, which tries to find the most compact sequence of instructions for executing the program.

If the four colour theorem is true, it means that it is always possible to perform the above operation on any graph and end with a sequence 111 or 222 in the end (or possibly both) by a number of intermixed expansions (when the number of faces increase by one) and contractions (when the number of faces decreases by one). If we can proof this property of the set of sequences, than we can proof the four colour theorem. If the four colour theorem is true, any intermediat set of sequences can be contracted in any possible way. If we could just proof that for each such set being expanded in any possible way, has the same property, then the four colour theorem is proven. On first sight this would not look very difficult at all, but that is not the case. I made some attempt to prove this, and discovered that it cannot be proven for just any set of sequences that can be contracted in any possible way. This mean, that one has to discover some property of the sets of sequences that can be reaced by any number of intermixed expansions and contractions. There are simply an infinite number of them.

I started with some simple cases and discovered that it is always possible to remove a face with four edges. This means that the Four colour theorem only needs to be proven for graphs with only faces with five or more edges. (I discovered today that this was already known by Alfred Kempe.) I wrote a progam to investigate the kind of sequences on robes around certain graphs. The main function for calculating this is given a number of points, a string representing the graph, and a number of rotations that it should generate sequences for. The string giving the graph uses letter starting from 'a' to label the graph. If a sequence of letter is followed by an equal sign, the function checks if the values for these point add up to zero modulo three. If it is followed by a comma or at the end of the string the value of the points modulo three is added. The values for which the function is called are:

- 8 points, "abcdh= defgh= ab,bc,cde,ef,fg,gha", and 1 rotation.
- 4 points, "a,ab,bc,cd,d,dcba", and 6 rotations.
- 4 points, "a,abc,cd,d,dcb,ba", and 6 rotations.
- 6 points, "abcde= ab,bc,cd,def,f,fea", and 6 rotations.
- 6 points, "abde= abc,c,cbd,def,f,fea", and 3 rotations.
- 6 points, "abdf= abc,c,cbde,e,edf,fa", and 6 rotations.
- 6 points, "abef= abc,cd,d,dcbe,ef,fa", and 6 rotations.
- 6 points, "abef= abcd,d,dc,cbe,ef,fa", and 6 rotations.

110112 * * ** * * * ** * * ** ** 112221 * * * * * * * ***** ** 112110 * * * * * * * ** * * * ** * 111222 * * * * * * * **** ** * 102102 * * * ** ** * * * * * * 102000 * * * * * * * * ** 101010 ** * * * * * * * * 000102 * * * * * * * * * * 000000 * * 001020 * * * * ** * * ** 012012 * * * ** ** * * * * * * 010002 * * * * * * * * * * 010101 * * * * * * ** * * 122211 * * * * * **** ** ** 122022 * * * * * ** * * * ** ** 101121 * * * * * * ** * * ** ** 011211 * * * ** * * * * * ** ** 121101 * * * * * * ** * * ** ** 120012 * * * * ** ** *** *** 100212 ** * * * * ** *** *** 001212 ** * * ** ** *** *** 012120 ** * * ** * ** *** ** 121200 ** * * ** ** ** *** * 121002 ** * * ** ** *** *** 120120 * * * ** * * * * ** * 100020 * * * * * * * * * 010200 * * * * * ** * * 110220 * * ** ** ** * * * ** * * 102201 * * ** ** ** * * * * * * * 011022 * ** ** ** * * * * * * ** 111111 *************** *This shows that there are many combinations of sequences that do meet the requirement that there is at least one of the sequences can be contracted in any possible way, but nevertheless do not contain one of the first thirteen sequences for the two joined faces with five edges (and five vertices).

- 5: How many people are in space right now.
- 5: Durovis Dive: Turning smartphone into virtual reality headset.
- 13: Spomenik - Works - Jan Kempenaers
- 13: Spomenik: Yugoslavian WW2 Memorials

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