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

Given FG5=4 then F5=1 or 3, but F5=3 requires E5=3 since EF5=6. That's not allowed, so E5=5, F5=1, and G5=3.

Similarly, ABC1=6, C34=4, and BC7=5 yield A1=1, B1=3, C1=2, B7=1, and C7=4.

That's all I have time for this morning.  This problem should be solved by the time I return this evening.

Posted by Mindrod on 2006-04-04 10:28:49