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
Solution without explanation
