Imagine you have a 5 x 5 grid. You have to place the numbers 1-25 on the grid so that each row, column and diagonal add up the the same number, can it be done?
For example, here's what I mean with a 3x3 version.
4 9 2
3 5 7
8 1 6
All columns, rows and diagonals all add up to 15.
I would love someone to work this out, been annoying me for ages.
My first step is to write out the numbers from 1 to 25 from left to right.
The second step is to flip the diagonals around the center number (which is 13).
The third step is to switch numbers to balance out the rows and columns in the 5 x 5 magic square (where all the rows, columns and diagonals sum to 65 in a normal 5 x 5 magic square).
Here's why it's so hard to work out. There are 275,305,224 distinct normal 5 x 5 magic squares. If it takes just a second to make one of them, how long would it take someone to make all of them? (for that matter, how many methods would one need to make all of them?)