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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?

 May 16, 2020
 #1
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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

 May 16, 2020

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