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PostPosted: Sat, 19 Mar 2011 17:18:18 UTC 
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S.O.S. Oldtimer

Joined: Sat, 31 Oct 2009 20:14:21 UTC
Posts: 158
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 bi-directional magic square (with respect to the second magic number).

Your challenge is to come up with an 8 x 8 bi-directional 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)


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 Post subject: Here's a hint
PostPosted: Sun, 17 Apr 2011 18:41:31 UTC 
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S.O.S. Oldtimer

Joined: Sat, 31 Oct 2009 20:14:21 UTC
Posts: 158
16 02 03 13
05 11 10 08
09 07 06 12
04 14 15 01

Please look at it carefully and compare. This should be enough to guide you.
To whomever solves this challenge I'll reveal a new discovery that I've recently made with the bi-directional magic square.

Good luck.


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 Post subject: One more hint
PostPosted: Sat, 23 Apr 2011 15:11:41 UTC 
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S.O.S. Oldtimer

Joined: Sat, 31 Oct 2009 20:14:21 UTC
Posts: 158
01 02 03 04
05 06 07 08
09 10 11 12
13 14 15 16

Now please carefully examine and compare. Somebody should be able to get an answer.


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