Rearrange the key caps of the 1 through 9 on a numeric keypad so that no cap is on its correct key, in such a manner that each of the three rows forms a 3digit perfect square.
789
456
123
361
529
784
The above three 3digit perfect squares are the only 3digit perfect squares where each nonzero digit appears.
The above arrangement is the sole arrangement. 529 cannot be on the bottom as the 2 would then remain in its original keypad position, nor can it be on the top as the 9 would remain in its original position, thus it must be in the middle. 784 cannot be on the top because the 7 and 8 would then remain in their original positions. As 529 must be in the middle, 784 must then be on the bottom row. The remaining 3digit number, 361, must then be on the top.
Edited on April 16, 2011, 2:46 am

Posted by Dej Mar
on 20110415 14:14:09 