Magic Square Solving Tips
Magic squares are arithmetic with structure. Rules first? See how to play.
1. One blank, one answer
A line with a single empty cell is solved by subtraction: the missing number is the total minus the rest. Scan rows, columns and diagonals for these first.
2. The centre of an odd square
In a 3×3 or 5×5 square the centre is the middle number (5 or 13), and cells opposite through the centre add up to n²+1 (10 or 26).
3. Complement pairs
In every size, numbers k and n²+1−k behave as a pair. If a line already holds a very high number, it needs low ones to balance; use the missing-number pad to see what is left.
4. Diagonals early
The diagonals touch the corners and the centre, which are the most constrained cells. Settle them and the rows and columns fall into place.
5. Bounds before guesses
Two blanks in a line must add up to a fixed amount; only a few pairs from the missing numbers fit. Try the pair, and let the crossing lines confirm or reject it.
Frequently asked questions
What is the quickest way into a 3×3 magic square?
The centre is always 5, and opposite cells always add up to 10. Place the 5, then fill each line that has two numbers by subtracting from 15.
Last updated 2026-10-21