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 Square division (Posted on 2006-08-24)
Here is a 8X8 square containing numbers 1 to 5 repeated four times. Can you divide the square into four similar shaped pieces such that each piece contains only one set of five numbers?
``` -------------------------------
| 1 |   |   |   |   |   |   | 1 |
-------------------------------
| 4 | 3 |   |   | 4 |   |   |   |
-------------------------------
|   |   |   |   | 5 |   |   | 2 |
-------------------------------
|   |   |   |   | 5 |   |   | 2 |
-------------------------------
| 3 |   |   | 5 | 5 |   |   |   |
-------------------------------
|   |   |   | 3 |   |   |   |   |
-------------------------------
| 4 |   | 2 | 2 |   |   |   |   |
-------------------------------
| 1 |   |   |   |   | 3 | 4 | 1 |
------------------------------- ```

 No Solution Yet Submitted by Salil Rating: 4.0000 (1 votes)

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 No Subject | Comment 12 of 13 |

My solution.  I know it's a repeat of brianjn's and Dej Mar's, but since I went to all the work of finding it, I couldn't resist posting.

` ------------------------------- | 1         |                 1 | |   ---------       ---------   | | 4 | 3           4 |       |   | |   |               |       |   ||   |             5 |       | 2 | |   ---------   -----       ----||           |   | 5           2 | |           ---------           || 3           5 | 5 |           | |----       -----   --------|   ||   |       | 3             |   | |   |       |               |   || 4 |     2 | 2             |   | |   ---------       ---------   || 1                 | 3   4   1 |  ------------------------------- `

I had an interesting hypothesis which turned out to be true.  Looking at the 5s near the middle, I knew they had to be divided, making part of a cross.  I completed that cross and guessed that the pieces would form rotational symmetry around the center.  So, I just replicated every cut that I knew I needed 3 more times around the center, and the solution quickly emerged.

 Posted by Ken Haley on 2006-08-29 01:41:56

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