Magic Square

How to play

A magic square is a grid filled with different numbers so that every row, every column and both long diagonals add up to the same total — the "magic constant". Some numbers are given; your job is to place the rest, using each number once. Tap an empty cell, then tap a number from the tray to drop it in. The running totals for every line update as you go, turning green when a completed line hits the target.

A 3×3 square uses the numbers 1–9 and every line totals 15. A 4×4 square uses 1–16 and every line totals 34.

Solving tips

• Start from the target. Each line must hit the magic constant, so a line that's missing one number tells you exactly which number goes there.
• The centre of a 3×3 is always 5. It's the middle value, and it sits on four different lines — a useful anchor.
• Corners and edges differ. In a 3×3, corners lie on three lines (row, column, diagonal) while edge-centres lie on two, which constrains which numbers can go where.
• Use the leftover set. Keep an eye on which numbers you haven't placed yet — often only one of them can complete a given line.

A little history

Magic squares are one of the oldest recreational puzzles there is. The 3×3 "Lo Shu" square appears in Chinese legend over two thousand years old, and Albrecht Dürer famously hid a 4×4 magic square in his 1514 engraving Melencolia I — with the year "1514" sitting in the bottom row. They've fascinated mathematicians and artists ever since, precisely because so much structure hides inside such a simple grid.

Frequently asked questions