What is the number in place of grey square ?
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For easy notation, a , b , c and d will denote the number in the green, orange, grey and yellow boxes respectively
From the picture, we can conclude that a + b = 8 , a + c = 1 3 , c − d = 6 and b + d = 8
From a + b = 8 = b + d , we get a = d by taking b away from both sides
Therefore c + d = 1 3 (by replacing a with d )
So we must find a pair of c and d that suffers the constraints c + d = 1 3 and c − d = 6
1 3 / 2 = 6 . 5 , so if the difference was 0 , then c would be 6 . 5
But the difference is 6 , so c and d should be bigger and smaller by 3 , respectively
6 . 5 + 3 = 9 . 5