If you ever need a 4-by-4 Magic Square,
here's an easy way to construct one.
Draw a 4-by-4 grid
and consider the cells on the two diagonals.
. . \(\displaystyle \begin{array}{|c|c|c|c|} \hline * &&& *\\ \hline& * & * & \\ \hline & * & * & \\ \hline * &&& * \\ \hline \end{array}\)
Starting at the upper-left, count 1, 2, 3, ...
and insert the numbers in the diagonal cells.
. . \(\displaystyle \begin{array}{|c|c|c|c|} \hline \color{red}{1} &&& \color{red}{4} \\ \hline& \color{red}{6} & \color{red}{7} & \\ \hline& \color{red}{10} & \color{red}{11} & \\ \hline \color{red}{13} &&&\color{red}{16} \\ \hline \end{array}\)
Now start at the lower-right, count 1, 2, 3, ...
moving up the square, and insert the numbers.
. . \(\displaystyle \begin{array}{|c|c|c|c|} \hline 1 & \color{red}{15} & \color{red}{14} & 4 \\ \hline \color{red}{12} & 6 & 7 & \color{red}{9} \\ \hline \color{red}{8} & 10 & 11 & \color{red}{5} \\ \hline 13 & \color{red}{3} & \color{red}{2} & 16 \\ \hline \end{array}\)
And there is the Magic Square!
Its magic sum is 34.
You will find "34" in various symmetric locations:
the 4 corner cells, the central 2-by-2 cells,
the 2-by-2s in each corner, and so on.
here's an easy way to construct one.
Draw a 4-by-4 grid
and consider the cells on the two diagonals.
. . \(\displaystyle \begin{array}{|c|c|c|c|} \hline * &&& *\\ \hline& * & * & \\ \hline & * & * & \\ \hline * &&& * \\ \hline \end{array}\)
Starting at the upper-left, count 1, 2, 3, ...
and insert the numbers in the diagonal cells.
. . \(\displaystyle \begin{array}{|c|c|c|c|} \hline \color{red}{1} &&& \color{red}{4} \\ \hline& \color{red}{6} & \color{red}{7} & \\ \hline& \color{red}{10} & \color{red}{11} & \\ \hline \color{red}{13} &&&\color{red}{16} \\ \hline \end{array}\)
Now start at the lower-right, count 1, 2, 3, ...
moving up the square, and insert the numbers.
. . \(\displaystyle \begin{array}{|c|c|c|c|} \hline 1 & \color{red}{15} & \color{red}{14} & 4 \\ \hline \color{red}{12} & 6 & 7 & \color{red}{9} \\ \hline \color{red}{8} & 10 & 11 & \color{red}{5} \\ \hline 13 & \color{red}{3} & \color{red}{2} & 16 \\ \hline \end{array}\)
And there is the Magic Square!
Its magic sum is 34.
You will find "34" in various symmetric locations:
the 4 corner cells, the central 2-by-2 cells,
the 2-by-2s in each corner, and so on.
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