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.

  | 6   0 |    -     1

  | 0   2 |     1   4

    -    5       2   -

    1    -     | 4   2 |    

 

The total sum on the pieces is 28, so each row and column must sum to 7. (4x7=28).  The (0,6) piece is inverted, but an upside down 6 is still a 6 (see note below puzzle).  The (2,4) piece in the lower right corner is also inverted.  Only the (0,2) piece is oriented in the "normal" fashion.  The remaining three pieces are on a diagonal, but the numbers on each of them fall within the rows and columns of the 4x4 box so that the sum of each row and column equals 7.           

Posted by Mindy Rodriguez on 2005-10-29 23:31:53