An 8-by-8 square is divided into 64 unit squares and each unit square is painted one of four possible colors. The ratio of the numbers of squares of each color is 1:2:3:x. How many integer values could x have?
+36916 1+2+3+x has to add to a factror of 64
factors 1 2 4 8 16 32 64
for one 1 +2+3+ 2 = 8
for another 1 + 2 + 3 + 10 = 16
another 1 + 2 + 3 + 26 = 32
and 1+ 2 + 3 + 58 = 64
