--- title: "Free magic square generator with answers | Once Books" description: "A free magic square generator that makes a printable puzzle and its answer in one click. Every puzzle has one completion, with no sign-up and no watermark." source: "https://www.oncebooks.com/tools/magic-square-generator" --- 1. [Home](https://www.oncebooks.com/) 2. [Tools](https://www.oncebooks.com/tools) 3. Magic square generator 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. PuzzleDesign 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. Theme ClassicBoldSoftShadedNavyIndigoSkyTealEmeraldForestPlumBerryCrimsonEmberAmberCocoa **Customise colours** Numbers Cell lines Box lines Page background Style StandardClean Clean drops the title band and footer, leaving the grid. Generate puzzlePrint / save PDF 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](https://app.oncebooks.com/publisher-studio/magic-square/edit?from=magic-square&v=2&s=eyJkaWZmaWN1bHR5IjoiTUVESVVNIiwiY29sb3JUaGVtZSI6eyJ0aGVtZUlkIjoiY2xhc3NpYyIsIm92ZXJyaWRlcyI6e319fQ) Free to build · pay once to export Preview The puzzle and its completed answer, as they print. Hide the preview - Magic Square Medium Every row, column and diagonal sums to 15 1 Puzzle - Magic Square Medium · Solution Every row, column and diagonal sums to 15 2 Solution Generate puzzlePrint / save PDF ## How to make a magic square 1. Pick 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. 2. Generate 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. 3. Print 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 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. ## 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](https://www.oncebooks.com/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](https://www.oncebooks.com/magic-square) and print one today.