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 the e*9 there is also the following variant:

4 3 5

9 2 8

6 1 7

Each of the three models (two in my first posting, and the one above) had a total of eight reflections, rotations, inversions, etc. Hence there are two pattern solutions for the e*9, but still only the one for e*7.

Posted by ed bottemiller on 2009-08-14 13:19:28