Fill a 10x8 matrix with 80 distinct integers between 1 and 160 (both numbers inclusive) so each of its ten rows adds up to 640, and each of its eight columns adds up to 800.

I think it's pretty straightforward to come up 2 X 4 matrixes which don't overlap, each of whose two rows add up to 320 and each of whose 4 columns add up to 160.  I only need ten of them, and I think I can even do it without using any of the 79 numbers between 41 and 119 (inclusive) .

Here's my first three sub-matrices:

  1   158 157   4
159   2    3   156

 5    154 153   8
155   6     7   152

  9   150  149   12
151   10   11  148

stacking these sub-matrices 5 high and two wide, in any order, satisfies the puzzle requirements. 

I think there is a very large number of solutions, and a lot of approaches that can be taken

Edited on July 16, 2006, 8:17 pm

Edited on July 16, 2006, 8:23 pm

Edited on July 20, 2006, 11:20 pm

Posted by Steve Herman on 2006-07-16 20:15:00