Making a 3x3 magic square that adds up to 1 I got this problem from my sister in 6th grade. I spent 3 hours on this and couldn't figure it out for the life of me.
You're given an empty 3x3 square. You have to fill it with numbers from -9 to 9. Columns and rows and diagonals add up to 1. You cannot repeat any number.
I can't seem to find any combination that would give sums of 1 for all of them. Is there some algorithm for this?
The teacher claimed that none of her students had been able to solve this problem the past 14 years she's given it to them.

Take a standard magic square and divide all of the numbers inside by $15$:
$$\begin{matrix}
  8/15 & 1/15 & 6/15 \\
  3/15 & 5/15 & 7/15 \\
  4/15 & 9/15 & 2/15
 \end{matrix}$$
Each entry is a (rational!) number between $-9$ and $9$.
