Nine consecutive integers are placed in the squares of a 3x3 grid.
Every column, every row, and every diagonal add up to the same number n and the middle number is 8.
What is n?
If each row adds up to n, then all 9 squares add up to 3n. Also, if we add up the four lines that pass through 8, we get the sum of all squares plus 3 additional 8s, or 3n+3×8. But this also adds up to 4n, since it is four groups of three that add up to n each.
Therefore 3n+3×8=4n, or n=24.
Here is one way to do it:
- Problem by Geoff Pilling
- Solution by Geoff Pilling
- Powered by