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

After tinkering around with this for a while, I have come up with the solution. Here is the completed grid (note that I am labeling the rows by A-G, top to bottom, and the columns by 1-7, left to right):

1234567 (col #s)

1542763 A

3657241 B

2713654 C

5321476 D

6174532 E

7436125 F

4265317 G

(Sorry about the line breaks - every time I hit ENTER my comment window skips a line for some reason!)

This was a tricky question! The crucial step that I had to take to find the answer involved analyzing the grid to find where the 1s had to be placed. I was able to prove that the DEF2=8 clue had to have a 1 placed in the middle - after that the rest seemed to fall out fairly easily. Good puzzle Percy - thanks! I wonder why it has received so few posts as yet? This seems like it would be a puzzle that would appeal to all the sudoku fans.

-John