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 4digit 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.
Since a square number terminates in 1, 4, 5, 6 or 9 and the right side column and lower row are the terminal cells of squares, the only 4 digit squares which contain only those digits are 1156, 1444 and 6561.
Now the problem does not say that all 9 nonzero digits must appear, nor does it say that any square number cannot be repeated.
With that in mind I offer:
2 1 1 6 46*46
1 2 2 5 35*35
1 2 9 6 36*36
6 5 6 1 81*81
This was derived using a spreadsheet. I also grouped all of the 4 digit squares according to their terminating digit to make my choices easier.
When I chose 1296 I then looked to see what squares terminated in "16" and "25". From then on it became quite clear what my remaining choices were to be.

Posted by brianjn
on 20091010 23:22:17 