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Yesterday, a friend of mine asked me for a number between 11 and 99 (not 100% sure about the boundaries). I had no idea what he was up to and called 38, about half a minute later he had written down the following:

$\begin{pmatrix} 18 & 1 & 12 & 7\\ 11&8&17&2\\5&10&3&20\\4&19&6&9 \end{pmatrix}$

At first, I thought it was already pretty impresive that all rows, columns and the two diagonals sum up to 38. Then he showed me that also the four 2x2 squares in the corners sum up to 38, and so do

$\begin{pmatrix} 1 & 12\\ 8 & 17 \end{pmatrix}, \begin{pmatrix} 8 & 17 \\ 10 & 3 \end{pmatrix} \text{ and } \begin{pmatrix} 10 & 3\\ 19 & 6 \end{pmatrix}.$

Does this "thing" have a name? How does one produce such a matrix in such a short amount of time?

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    @fleablood: I don't think anything was edited at all?2016-04-08

1 Answers 1

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(A compilation of some comments...)

These are called "Magic Squares".

Wikipedia

Here's how to create a magic square for any number