Place twelve of the numbers 1 to 15 in the grid below such that:
1. The rows (a,b,c,d; e,f,g,h; i,j,k,l) have the same sum.
2. The columns (a,e,i; b,f,j; c,g,k; d,h,l) and the diagonals (a,f,k; b,g,l; c,f,i; d,g,j) all have the same sum.
Note: The rows do not have the same sum as the columns and diagonals.
a|b|c|d
-+-+-+-
e|f|g|h
-+-+-+-
i|j|k|l
If I had to guess... I'd say there were 8 solutions.
But they have duplicates (if you count mirrors and rotations), so only the first two are truly different solutions.
3 is a rotation of 2
4 is a rotation of 1
8 is a mirror of 1
7 is a mirror of 2
5 is a rotation of 8
6 is a rotation of 7
and the following is what I think they are:
1 11 5 15
14 10 6 2
9 3 13 7
1 13 3 15
11 9 7 5
12 2 14 4
4 14 2 12
5 7 9 11
15 3 13 1
7 13 3 9
2 6 10 14
15 5 11 1
9 3 13 7
14 10 6 2
1 11 5 15
12 2 14 4
11 9 7 5
1 13 3 15
15 3 13 1
5 7 9 11
4 14 2 12
15 5 11 1
2 6 10 14
7 13 3 9
Edited on January 8, 2004, 8:22 pm
solution
