What is a magic square?

A magic square is a grid filled with each number from 1 to N² once, so that every row, every column and both main diagonals add up to the same total. That total, the magic constant, is printed under the grid.

Is this magic square generator free?

Yes. Pick a difficulty, generate a puzzle and print the grid plus its answer, with no sign-up and no watermark. It is free for classroom, home and personal use.

Does every puzzle have one solution?

Yes. Every puzzle is generated and checked by the same solver our Publisher Studio uses, so the given numbers fix exactly one completion. A puzzle is never ambiguous or unsolvable.

Does it include the answer?

Yes. Every puzzle prints as two pages: the puzzle on page one and the completed square on page two, so you can check your work.

What size are the pages?

The free tool prints at 8.25 by 11 inches, a popular large-print size. Our Publisher Studio will export the same book at any KDP trim, from 5.06 by 7.81 up to 8.27 by 11.69, as a print-ready 300 DPI interior.

Free tool

Free magic square generator, with the answer

Pick a size and generate a magic square, then print it with its answer. Every puzzle has one completion, with no sign-up and no watermark. It runs on the same engine as our KDP Publisher Studio.

Difficulty

Larger grids with fewer givens are harder. Every puzzle has one completion.

3×3 grid. Fill it with 1 to 9 so every row, column and diagonal sums to 15.

Two pages: the puzzle and its completed answer. Every puzzle has one solution, checked by the same engine as our KDP studio.

Want the whole book?

This makes one puzzle. Sign up to turn it into a full Magic Square book for Amazon KDP: hundreds of graded puzzles at any trim, as print-ready PDFs.

Build the full book

Free to build · pay once to export

Preview

The puzzle and its completed answer, as they print.

Magic Square Medium

Every row, column and diagonal sums to 15

1
Magic Square Medium · Solution

Every row, column and diagonal sums to 15

2

How to make a magic square

1Pick a difficulty. Choose a grid size from a gentle 3 by 3 up to a 5 by 5. Larger grids and fewer given numbers take longer to work out.
2Generate the puzzle. Press Generate puzzle. You get a grid with some numbers filled in and the magic total printed beneath it. Every puzzle has exactly one completion.
3Print the two pages. Press Print / save PDF. You get two pages: the puzzle on page one and the completed grid on page two.

How to solve a magic square

Fill the grid with each number from 1 to N² once so every row, column and both diagonals add up to the same total.

The method

1Find the magic total. For an N by N grid the total is N × (N² + 1) ÷ 2, printed under the grid, so a 3 by 3 is 15 and a 4 by 4 is 34.
2Start where a line is nearly full. A row, column or diagonal with only one empty square is forced: the missing number is the total minus the others.
3Use each number once. Every value from 1 to N² appears exactly once, so cross off numbers as you place them and you narrow the choices fast.
4Cross rows with columns. A square has to satisfy its row, its column and any diagonal it sits on. Where only one unused number fits all of them, lock it in.

The one rule: Use 1 to N² once each so every row, column and both diagonals share the same sum.
What the answer page shows: The fully completed square is printed at the back.
How the grades differ: Bigger grids and fewer given numbers mean more to deduce before the grid settles.
Good for: Solvers who enjoy arithmetic and a tidy, self-checking grid.

Publishing a whole book?

This tool makes one puzzle for home or the classroom. To make a magic square book you can sell on Amazon KDP, Publisher Studio generates hundreds of graded puzzles across a difficulty curve, at any KDP trim, as a print-ready interior and solutions PDF.

See the KDP magic square maker

Questions

What is a magic square?: A magic square is a grid filled with each number from 1 to N² once, so that every row, every column and both main diagonals add up to the same total. That total, the magic constant, is printed under the grid.
Is this magic square generator free?: Yes. Pick a difficulty, generate a puzzle and print the grid plus its answer, with no sign-up and no watermark. It is free for classroom, home and personal use.
Does every puzzle have one solution?: Yes. Every puzzle is generated and checked by the same solver our Publisher Studio uses, so the given numbers fix exactly one completion. A puzzle is never ambiguous or unsolvable.
Does it include the answer?: Yes. Every puzzle prints as two pages: the puzzle on page one and the completed square on page two, so you can check your work.
What size are the pages?: The free tool prints at 8.25 by 11 inches, a popular large-print size. Our Publisher Studio will export the same book at any KDP trim, from 5.06 by 7.81 up to 8.27 by 11.69, as a print-ready 300 DPI interior.

Short of ideas? Browse our ready-made printables for this puzzle and print one today.