Look at this magic square (please verify that its rows, columns and diagonals sum up to 34):
11 05 08 10
02 16 13 03
14 04 01 15
07 09 12 06
This magic square has an amazing property whereby dot multiplying by 1,2,3 and 4 on each row or column yields 85. For example, with the first row you can dot multiply as follows: 1 x 11 + 2 x 5 + 3 x 8 + 4 x 10 = 85 which yields the same result for all the other rows and columns (so 85 is the second magic number for this square).
When you reverse dot multiply by 4,3,2 and 1, you still get 85 as the result for all the rows and columns (but not the diagonals which makes this magic square semimagic with respect to the second magic number of 85). This reverse dot multiplication means you can go from right to left (and from bottom to top) which makes this a bidirectional magic square (with respect to the second magic number).
Your challenge is to come up with an 8 x 8 bidirectional magic square based on the numbers 1,2,3,4,5,6,7 and 8 and specify what the second magic number is (by the way, I came up with six myself).
Are you up to the challenge? (better keep a bottle of Tylenol handy for your computer)
