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 Latin Square (Posted on 2006-04-04)
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

 No Solution Yet Submitted by Sir Percivale Rating: 3.5000 (4 votes)

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 Solution without explanation | Comment 2 of 4 |

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

 Posted by John Reid on 2006-04-04 23:09:49

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