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.