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?
(In reply to
Solution (by hand) by Guest)
Guest, can you explain how your solution is the unique one?
Except for no proof as a unique solution, the following also results in the correct totals:
X=9
1734
3113
8723
87X5
X=6
1563
3113
7724
99X5
I suspect only one solution exists for one of the possible values of X. While the possible values of X has two or more solutions. The smudged value will be the one with a single solution.
Edited on June 5, 2007, 1:12 am

Posted by Dej Mar
on 20070605 00:28:31 