# Franklin magic square

One day in 1771, Benjamin Franklin, tired of hearing political debates, amused himself by creating the following magic square, now called a Franklin magic square:

 $\begin{bmatrix}52&61&4&13&20&29&36&45\\ 14&3&62&51&46&35&30&19\\ 53&60&5&12&21&28&37&44\\ 11&6&59&54&43&38&27&22\\ 55&58&7&10&23&26&39&42\\ 9&8&57&56&41&40&25&24\\ 50&63&2&15&18&31&34&47\\ 16&1&64&49&48&33&32&17\\ \end{bmatrix}$

The magic constant is 260. Furthermore, half any row or column (positions 1 to 4 or 5 to 8) equals half the magic constant. Two centuries later, Joseph Madachy realized that some half diagonals from the corner to the center also give 260.

Some other 8 by 8 magic squares with these properties are also called Franklin magic squares.

Title Franklin magic square FranklinMagicSquare 2013-03-22 16:24:52 2013-03-22 16:24:52 PrimeFan (13766) PrimeFan (13766) 4 PrimeFan (13766) Example msc 05B15 msc 01A50 Franklin square