MHB How to Create 4-by-4 Magic Square w/Sum 34

[soroban]

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.

$\quad\begin{array}{|c|c|c|c|} \hline
* &&& *\\ \hline
& * & * & \\ \hline
& * & * & \\ \hline
* &&& * \\
\hline \end{array}$Starting at the upper-left, count 1, 2, 3, ...
and insert the numbers in the diagonal cells.

$\quad\begin{array}{|c|c|c|c|} \hline
\color{red}{1} &&& \color{red}{4} \\ \hline
& \color{red}{6} & \color{red}{7} & \\ \hline
& \color{red}{10} & \color{red}{11} & \\ \hline
\color{red}{13} &&&\color{red}{16} \\ \hline
\end{array}$Now start at the lower-right, count 1, 2, 3, ...
moving up the square, and insert the numbers.

$\quad\begin{array}{|c|c|c|c|} \hline
1 & \color{red}{15} & \color{red}{14} & 4 \\ \hline
\color{red}{12} & 6 & 7 & \color{red}{9} \\ \hline
\color{red}{8} & 10 & 11 & \color{red}{5} \\ \hline
13 & \color{red}{3} & \color{red}{2} & 16 \\ \hline \end{array}$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.

 

[lofgran]

Hello, thank you for sharing this easy method for constructing a 4-by-4 Magic Square! I find this type of problem-solving very interesting.

For those who may not be familiar with Magic Squares, they are a type of grid filled with numbers where the sum of each row, column, and diagonal is the same. In this case, the magic sum is 34. These types of puzzles have been around for centuries and have fascinated mathematicians and scientists with their patterns and properties.

Your method is a great way to quickly construct a Magic Square without having to rely on complicated mathematical formulas. It also highlights the symmetry and patterns that exist within the square, which is a common feature in Magic Squares.

I would also like to add that there are many other methods for constructing Magic Squares, some of which involve using algebraic equations or even computer algorithms. It's always interesting to explore different approaches and see how they compare.

Thank you again for sharing this method, I'm sure it will be useful for anyone looking to create a 4-by-4 Magic Square. Keep exploring and solving puzzles!