Brain Teaser

Question

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?


Answer

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
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