---
title: "Printable magic squares: free, with answers | Once Books"
description: "Free printable magic squares. Fill the grid with 1 to N² so every row, column and both diagonals sum to the same total, and every puzzle has one completion. Print with the answer."
source: "https://www.oncebooks.com/magic-square"
---

Free printables

# Free printable Magic square with answers

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. Fill the blanks using the given numbers and that single total. Every puzzle here has exactly one completion.

## By size

Size is what makes a magic square harder: a bigger grid uses more numbers and a larger total, and fewer givens leave more to deduce. Start on a 3 by 3 and work up to a 5 by 5.

- [Easy magic square](https://www.oncebooks.com/magic-square/easy) — Free printable easy magic squares with answers. A gentle 3 by 3 grid with most numbers given, each summing to 15. No sign-up.
- [Medium magic square](https://www.oncebooks.com/magic-square/medium) — Free printable medium magic squares with answers. A 3 by 3 grid with fewer givens to deduce, each with one completion. Print with the answer.
- [Hard magic square](https://www.oncebooks.com/magic-square/hard) — Free printable hard magic squares with answers. A 4 by 4 grid using 1 to 16, each line summing to 34. One completion, printed with the answer.
- [Large magic square](https://www.oncebooks.com/magic-square/large) — Free printable large magic squares with answers. A 5 by 5 grid using 1 to 25 for a long solve, with the completed grid on page two. No sign-up.

## By audience

A smaller grid with more numbers given uses the same rule, as a gentle introduction for a child or a beginner.

- [Magic squares for kids](https://www.oncebooks.com/magic-square/for-kids) — Free printable magic squares for kids with answers. Small 3 by 3 grids that practise adding to 15, each with one completion. No sign-up.
- [Magic squares for beginners](https://www.oncebooks.com/magic-square/for-beginners) — Free printable magic squares for beginners with answers. Small grids to learn the rule, each with one completion. Print with the answer.

## One answer, every time

The thing that makes a magic square book worth printing is the guarantee most sellers cannot make: that the given numbers fix exactly one completion. Every puzzle is generated by building a true magic square, blanking cells, and running a solver that proves one completion survives. The filled grid prints as the answer key.

## 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

1. Find 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.
2. Start 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.
3. Use 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.
4. Cross 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.

## Make one now

Pick a size from a gentle 3 by 3 up to a 5 by 5, then print the puzzle and its answer. No sign-up, no watermark.

[Open the magic square generator](https://www.oncebooks.com/tools/magic-square-generator)[Make a whole book for KDP](https://www.oncebooks.com/kdp-magic-square-maker)