Reverse engineering a math magic trick involving matrices.
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This problem was brought up by my mother from a corporate party along with a question on how that worked. There was a showman who asked to tell him a number from $10$ to $99$ (If i'm not mistaken). The number $83$ was named after which he took a piece of paper and quickly put down a matrix (note he did that fast): $$ begin{bmatrix} 8 & 11 & 63 & 1\ 62 & 2 & 7 & 12\ 3 & 65 & 9 & 6 \ 10 & 5 & 4 & 64 end{bmatrix} $$ If you take a closer look every row, column and diagonal has the sum of $83$ . Moreover consider the corners of the matrix also have the sum of $83$ . For example: $$ begin{bmatrix} colorred{8} & colorred{11} & 63 & 1\ colorred{62} & colorred{2} & 7 & 12\ 3 & 65 & 9 & 6 \ 10 & 5 & 4 & 6