Place 16 nonzero base ten digits in the cells of a 4x4 square grid, with each digit occurring in a cell exactly once. The digits can be considered as forming eight 4-digit numbers, read left to right and top to bottom, each of which is a perfect square. Since there are more than nine cells, there will be an obvious repetition of digits.

Are you sure all digits have to be nonzero?  If so, the only possible numbers for the right column and bottom row are 1156, 1444, and 6561 (since all squares end in either 1, 4, 5, 6, or 9).  But none of these three numbers end with the same digit, so what would go in the bottom right cell?  (Or maybe I overlooked something?)

Posted by Jim Keneipp on 2009-10-10 13:53:28