Each cell in a grid contains one of the digits from 1 to 7. Each row and column has each digit exactly once. The following clues give the totals of the cells indicated. How can you fill the grid?

A56=13
ABC1=6
ABCD4=13
B234=18
BC7=5
C34=4
D67=13
DEF2=8
EFG3=16
EF5=6
FG5=4
G1234=17

(In reply to A starting point by Mindrod)

   A B C D E F G
1  1 3 2 5 6 7 4
2  5 6 7 3 1 4 2
3  4 5 1 2 7 3 6
4  2 7 3 1 4 6 5
5  7 2 6 4 5 1 3
6  6 4 5 7 3 2 1
7  3 1 4 6 2 5 7

I'm surprised it took so long for a solution to be posted.  I honestly thought it would be solved long before I returned.  Here's my solution starting from where I left off.  I see that it is identical to John Reid's solution (good work John).

Posted by Mindrod on 2006-04-05 10:26:44