Every row, column and diagonal must total: 15
Numbers to place:
Pick a number, then tap a cell
| Pick a number | Choose from the pool. |
| Tap a cell | Place it there. |
Number Grid is a magic square. Place every number in the grid so that each row, each column and both diagonals add up to the same total. Every number is used exactly once, and there is only one arrangement that works up to rotation.
Magic squares are among the oldest recreational mathematics there is, appearing in Chinese texts more than two thousand years ago. The three by three version has exactly one solution ignoring rotations and reflections, and finding it by reasoning rather than trial and error is deeply satisfying.
Work out the target total first. It is the sum of all the numbers divided by the number of rows, and knowing it turns the puzzle from guesswork into arithmetic you can check as you go.
The centre cell is forced. In a three by three magic square the middle number is always the average of the whole set, which for one to nine means five. Placing that first collapses most of the difficulty.
The corners take the even numbers. Once the centre is fixed, the even numbers go in the corners and the odd ones on the edges. That single pattern gets you most of the way to a solution.
Check diagonals as you go, not at the end. It is easy to build rows and columns that work and discover the diagonals do not, so verifying all three directions as you place each number saves rework.
A grid where every row, column and diagonal adds up to the same total, using each number exactly once.
Add all the numbers and divide by the number of rows. For one to nine in a three by three grid, that is fifteen.
For the three by three square, yes, ignoring rotations and reflections.
Very. They appear in Chinese mathematical texts over two thousand years old.
No. Number Grid runs entirely inside this page, so it starts the moment the page opens. There is nothing to download, no plugin, and no account to create.