Magic Square
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Magic Square

MathsNumber gridSingle playerProof by sum

Fill the gaps so every row, column and diagonal adds up to the same number.

Controls — Tap a cell and type a number. No keyboard shortcuts needed.

How to play

  1. Each square hides a few cells. Fill them so every row, column and both diagonals share one sum.
  2. The target is shown: 15 for 3 × 3, 34 for 4 × 4.
  3. Cells turn red when a line can no longer reach the target — that is your signal to back up.

Tips

  • The centre of a 3 × 3 is always one third of the target: 5.
  • Pairs opposite the centre add up to one more than the side length squared — 10 in a 3 × 3.
  • In a 4 × 4, the four corners and the four centre cells also sum to 34. Use that as a check.

About this game

Magic squares are old enough to appear in Chinese and Islamic art long before they were called puzzles. The 3 × 3 is unique up to rotation and reflection; the 4 × 4 has 880 essentially different solutions.

This version builds both sizes from scratch — the Siamese method for odd squares, complement pairs for multiples of four — then hides a few cells and lets you finish it.

No download, no account, no tracking, no ads.

FAQ

Can a number repeat?

No. Each number from 1 to the square of the size is used exactly once.

Why no 6 × 6?

Singly even squares need a third construction (the LUX method). It is a different puzzle, not a bigger one.

What does Reveal do?

Fills the whole square. It is there to check your reasoning, not to score.

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