A 5x5 grid has been colored in such a way that any group of cells consisting of a cell and its two, three or four neighboring cells has each of its cells being of a different color. This has been done in such a way as to use the minimum possible number of colors that will accomplish that. Two of the red cells have been shown in the diagram below. Which of the other numbered cells are also red?

1	2	3	4	5
6	7	8	9	10
11	12	13	14	15
16	17	18	19	20
21	22	23	24	25

As each cell and its orthogonal neighbors are comprised of different colors, the minimum number of colors is five. The arrangement, given five colors and given that square 1 and 23 are both red (R) are:
R a b c d
b c d R a
d R a b c
a b c d R
c d R a b
The numbered locations of the red colored squares other than the givens 1 and 23 are 9, 12, and 20.

Posted by Dej Mar on 2011-10-26 14:59:22