Pfister's sixteen-square identity

Imagine you have 16 boxes, all lined up in a 4 x 4 grid. These boxes can have numbers in them. Now, let's say you want to find the sum of all the boxes in each row, column or diagonal.

The sixteen-square identity is a mathematical formula that helps you find the sum of these boxes very easily. It says that no matter which row, column, or diagonal you choose, the sum will always be the same!

Here's how it works:

Let's call the sum of all the numbers in the boxes "S". Now, let's take any row, column or diagonal, and add up all the numbers in it. Let's call the sum of that row, column or diagonal "X".

Then, the sixteen-square identity says that:

S = 4X

What does this mean? It means that if you add up all the numbers in all the rows, columns and diagonals of the 16 boxes, you will get a certain number. Let's say that number is 100.

Then, if you take any row, column, or diagonal and add up all the numbers in it, you will get a certain number. Let's say you choose the first column and add up all the numbers in it. Let's say that number is 20.

Now, according to the sixteen-square identity, we know that:

S = 4X
100 = 4(20)

So, the sum of all the numbers in the boxes is 100, and the sum of the numbers in the first column is 20.

This formula makes it really easy to find the sum of any row, column or diagonal without having to actually add up all the numbers in it!