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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
 my solution Comment 4 of 4 |
I made my grid with rows A-G from top to bottom and columns 1-7 from left to right.

1.) Given that EF5=6 and FG5=3, E5 has to be 5, F5 has to be 1, and G3 has to be 3.

2.) Since C34=4, the numbers must be 1,3 or 3,1. Since ABC1=6 and BC7=5, then C1 must=2 and C7 must = 4.  So obviously, B7=1, B1=3 and A1=1.

3.) EFG3=16.  From this, all possible number combinations, from top to bottom are: 3,6,7 | 3,7,6 | 4,5,7 | 4,7,5 | 5,4,7 | 5,7,4 | 6,3,7 and 6,7,3 and 7,3,6   The two 5 combinations as well as the final one can be eliminated because of the 5,1,3 directly to the right.

4.) C3 must be either 1 or 3. If it is three, the grid does not work out about 3/4 of the way through. I ended up with 2, 3's in one row. So it has to be 1, which means C4=3.

5.) B234=18  This means the numbers must be 5,6 and 7.  In any combination, if B4= 5,6 or 7, one of the remaining squares must= 1 in order for ABCD4=13.  So D4 must be 1 in any case.

6.) E2 must be 1 becuase 1,2,5 and 1,3,4 are the only possible cobinations of 8. Both have a 1 and E2 is the only possible spot.

7.) For DEF to equal 8, there are 4 possible combinations with E2 being 1. 4,1,3 | 3,1,4 | 5,1,2 | and 2,1,5. None work out except 3,1,4.

8.) From here, it is easy. D1 must be 5, G1 must be 4 because the combinations for 6 and 7 do not work out.

I got:

1542763
3657241
2713654
5321476
6174532
7436125
4265317

Nice puzzle :)

 Posted by Bourne Chase on 2006-07-01 01:29:57

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