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Saturday, August 2, 2014

A Five By Five Magic Square

A few years ago I wanted to find a 5 by five magic square. I gave up on it. See this post for the results I came up with in 2011. I used the wrong tools, I can see that clearly now.

Yesterday and today I worked on it. Again without finding a solution. This morning I thought "Should I spend another day on it? What am I doing with my time? I am not going to solve this one ( either )". But problems you can't solve become little traumas in your subconscious. From time to time they remind you that you weren't able to crack them. It hurts. Probably more than you can imagine.

There was one thing I could add to my search algorithm, I decided to add that and then stop. I had only one diagonal left that didn't add up to 65. Anyway, the last thing worked and I found one. One hurting trauma less.

2 & 25 & 5 & 20 & 13 \\
18 & 4 & 17 & 7 & 19 \\
8 & 24 & 22 & 10 & 1 \\
23 & 9 & 6 & 16 & 11 \\
14 & 3 & 15 & 12 & 21

The integers $1,2 \dots 25$ are laid out in a 5 by 5 matrix such that the rows, columns and the two diagonals total to 65.

Now the real fun begins: finding bigger ones, special ones maybe, and analyzing and optimizing my method. Where are the limits? And questions, many questions like how many different 5 by 5s are there? Is there one with the number 13 in the centre?

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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)