In the example below, three rectangular pieces of dimensions 2x1, with the numbers (0,5), (2,3) and (2,3) are put into the 3x3 box so that all the 6 sums (3 rows and 3 columns) are the same (=5).

               +---------------------+
               |       +=====++=====+|
               |       |  2  ||  3  ||
               |+=====+|-----||-----||
               ||  0  ||  3  ||  2  ||  
               ||-----|+=====++=====+|
               ||  5  |              |
               |+=====+              | 
               +---------------------+

I put these six similar pieces - (0,2), (0,6), (1,1), (1,5), (2,4) and (2,4) - with the numbers upwards, in a 4x4 box and showed it to my next door neighbour. He noticed that all 8 sums (4 rows and 4 columns) added up to the same number. How did I do it?

           +=====+=====+ +=====+=====+ +=====+=====+
           |  0  |  2  | |  0  |  6  | |  1  |  1  |
           +=====+=====+ +=====+=====+ +=====+=====+ 
           +=====+=====+ +=====+=====+ +=====+=====+
           |  1  |  5  | |  2  |  4  | |  2  |  4  |
           +=====+=====+ +=====+=====+ +=====+=====+

Note: the "6" shown is still a "6" even when you put that piece upside down.

Lay 5 of the pieces as follows:

 +-------+
 | 2 | 4 |
 +-------+---+ 
 | 4 | 2 | 2 |
 +-------+ - +---+
         | 0 | 6 |
     +---+---+ - |
     | 1 | 5 | 0 |
     +-------+---+

Then put the (1,1) piece on top of the two 2's 
in the 2nd row as follows:


 +-------+
 | 2 | 4 |
 +---+---+---+ 
 | 4 | 1 | 1 |
 +---+---+---+---+
         | 0 | 6 |
     +---+---+ - |
     | 1 | 5 | 0 |
     +-------+---+

and then all the rows and columns add up to 6

 

Edited on October 26, 2005, 11:25 am

Posted by Lisa on 2005-10-26 11:24:58