Susan was about to have her puzzle published as New Scientist's Enigma for the week when she discovered that one of the numbers she had prefilled in was smudged beyond recognition. It looked like this:
"Fill in each of the empty spaces with a nonzero digit so that the rows, columns and diagonals add up to the totals shown:
     20 
 1     15 
    3  8 
  7    20 
   X   29 
 20  22  15  15  9 
please send the completed grid."
where the numbers at the bottom represent the sums of the columns in the 4x4 grid; those at the right represent the totals of the rows; the 9 at the lower right is the sum of the main diagonal and the 20 at the upper right represents the total of the diagonal going from lower left to upper right.
The x represents the smudged digit.
The puzzle Susan had in mind had only one solution. Can you find that solution?
With small limitation calculation we can arrive to these possible 6 combintions
1 4
2 2 1 3
9 7 1 3
8 X 5
1 3
2 2 1 3
8 7 1 4
9 X 5
1 3
2 1 2 3
9 7 1 3
8 X 6
1 2
2 1 2 3
8 7 1 4
9 X 6
1 5
3 1 1 3
9 7 2 2
7 X 5
1 4
3 1 1 3
8 7 2 3
8 X 5
1 4
3 1 1 3
8 7 2 3
8 X 5
But only in case 4 which is
1 2
2 1 2 3
8 7 1 4
9 X 6
if you can have a unique value of x = 5. and thus resulting in a unique solution.

Posted by Sachin
on 20070709 17:33:24 