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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 3-digit perfect square.
```
789
456
123
```

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 solution | Comment 2 of 4 |

361
529
784

The above three 3-digit perfect squares are the only 3-digit perfect squares where each non-zero 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 3-digit number, 361, must then be on the top.

Edited on April 16, 2011, 2:46 am
 Posted by Dej Mar on 2011-04-15 14:14:09

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