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.

(In reply to impossible? by Josh70679)

Yeah, I've thought of that too. But the numbers can lie next to eachother so Im thinking that the sum on all edges would be something like 8

Posted by Quincy on 2005-10-27 13:21:21