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 Congratulations. by Mindrod)

I noticed, Mindy. But I couldnīt state this at that time, for obvious reasons. In fact, Gamer said to me that he had found an alternative answer, but he didnīt post it.

Itīs not the first time that she has the correct "insight" to solve some problems. So, Iīm joining you to congratulate Lisa.

Though this is not a "competition site", I think too that the first to achieve an answer (not a computer-obtained solution in some problems) should be mentioned when posted the "official" solution, though the others donīt think the same.

Edited on November 8, 2005, 7:06 am

Posted by pcbouhid on 2005-11-08 06:59:29