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

Oops.  The first of the two arrangements I posted didn't work.  The arrangements that do have all neighboring cells colored differently are

Posted by Steve Herman on 2011-10-26 20:20:55