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Square division (Posted on 2006-08-24) Difficulty: 4 of 5
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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