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 | 
 ------------------------------- 

 
    1 1
    1
 1 1    1
    1 1 1
          1
 0 0    1
    1 1 1


This is the shape to which I referred in my last comment.
The zeroes in the second last line may be shared or passed over to the adjoining shape.  Whichever, there are three solutions by my reckoning.
 

Edited on August 24, 2006, 11:28 pm

Posted by brianjn on 2006-08-24 23:28:20