Substitute each of the capital letters in bold in this 3x3 grid by a different digit from 1 to 9 such that the sum of digits in each of the four 2x2 subgrids is equal to 9*E.

A   B   C
D   E   F
G   H   I

What will be the arrangement(s) (disregarding reflections and rotations), if keeping all the other conditions unchanged, the sum of digits in each of the four 2x2 subgrids is equal to 7*E?

For E*9 = 18 (all solutions have E=2)

3 4 5

9 2 7

6 1 8

For E*7 = 14 (all solutions have E=3)

1 8 4

9 3 6

2 7 5

(Other solutions are rotations, permutations, etc.). 

Posted by ed bottemiller on 2009-08-14 12:59:05