Freudenthal magic square

A Freudenthal Magic Square is like a very special puzzle that has numbers in it. But not just any numbers! The numbers in a Freudenthal Magic Square are really special because they have to follow certain rules.

Imagine you have a square with nine boxes in it, arranged in a 3x3 grid. Each box can have a different number from 1 to 9 in it. The goal is to arrange the numbers in such a way that all three rows, three columns, and two diagonals of the square add up to the same number. That number is called the "magic constant."

But there's a catch! In a Freudenthal Magic Square, you also have to make sure that certain pairs of numbers in the square add up to specific other numbers. For example, if number 1 is in the top left box, then the number in the bottom right box must be 8, because 1+8=9. Similarly, if 2 is in the top middle box, then the number in the bottom middle box must be 7, because 2+7=9. These pairs of numbers are called "magic pairs."

So to solve a Freudenthal Magic Square, you have to figure out how to arrange the numbers so that they add up to the magic constant AND all the magic pairs are satisfied. It can be a tricky puzzle, but it's really satisfying when you solve it!