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Magic squares
Place 1 through 9 in a 3×3 grid so every row, column and diagonal adds to the same number.
3×3 Magic Square
Fill with 1–9 (each once) so every row, column and diagonal sums to 15.
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↘ diagonal: 0
↙ diagonal: 0
Show one solution
2
7
6
9
5
1
4
3
8
Why 15?
The numbers 1 + 2 + 3 + … + 9 add up to 45. There are 3 rows that must each sum to the same value, and they cover every cell once. So each row sums to 45 ÷ 3 = 15.
Where the 5 lives
The center cell appears in 4 of the 8 lines (row, column, two diagonals). For the math to balance out, the center has to be 5 — the middle of 1–9.
A famous arrangement
The Lo Shu square (an ancient Chinese arrangement) puts 5 in the middle, evens in the corners, odds on the sides. Once you place 5 and the corners, the rest follows.
Bigger magic squares
A 4×4 magic square uses 1–16 and each line sums to 34. A 5×5 uses 1–25 and sums to 65. The general formula for an n×n magic square built from 1 to n²: each line sums to n(n² + 1) / 2.