3–9 Order Magic Squares: Play & Explore

A magic square turns a simple grid into a test of arithmetic and observation. Explore normal squares, compare their line sums and use the free workshop tools without an account.

Magic square practice

Use each integer from 1 to 9 once. Every row, column and both diagonals must sum to 15.

Given clues are locked. Fill the empty cells, check your work, or reveal one hint.

Magic constant: 15

Number board

One target across the whole grid

A normal magic square uses every integer from one to the number of cells exactly once. Each row, each column and the two main diagonals must have the same sum. The target is not chosen at random: for an order n square it is n(n²+1)/2, obtained by dividing the total of all numbers among n rows. Checking only the rows is not sufficient, because a rearrangement may satisfy those sums while breaking a column or a diagonal.

Choose an order and learn its structure

Begin with a three by three grid to work with nine numbers and a target of fifteen. Move to four by four to explore complement patterns, then five by five for a larger odd-order construction. A nine by nine magic square uses eighty-one different numbers and has a target of three hundred and sixty-nine. It is not Sudoku: there is no rule requiring repeated digits or separate three by three boxes. Every order page has its own explanation and a board you can edit and check.

Use the workshop for different jobs

The solver searches normal three by three squares that respect the clues you enter. For larger orders it offers line deductions and validation, not an unlimited search. The calculator gives the target, cell count, total and complement value for a chosen order. The generator constructs valid examples with rotations and reflections rather than claiming to list every possible square. These tools serve different questions, so use the page that matches your task and compare the result against all the line constraints.

Keep your reasoning visible

Start with a line that has one empty cell and subtract the filled values from the target. Check whether the missing number is still available and whether it fits the crossing line. When there is no forced move, keep candidate values separate instead of overwriting clues with a guess. The tutorial presents this as a four-step routine. All workshop tools are free and run in your browser. The Chinese archive also offers a local progression game, daily challenges and downloadable score cards. Its records stay on that browser and domain; no online account, shared ranking or cross-domain progress transfer is provided.