Magic Square Game Online Free
Use each number once so that every row, every column and both diagonals add up to the same magic sum. The totals update as you go.
Tap a square, then tap a number or type it (two digits quickly for 10 and up). Totals turn green when a line is right.
What is a magic square?
A magic square is a grid filled with the numbers 1, 2, 3 and so on, each used once, so that every row, every column and both main diagonals add up to the same total, called the magic sum. For a 3 × 3 square using 1 to 9 the magic sum is 15; for 4 × 4 it’s 34, and for 5 × 5 it’s 65.
Magic squares are thousands of years old: the Lo Shu square appears in Chinese legend, and Albrecht Dürer hid a 4 × 4 square in his 1514 engraving Melencolia I. In this magic square puzzle online, some numbers are given and there is exactly one way to finish. For more addition puzzles, try Kakuro or the 24 Game.
How to play Magic Square Game
- Fill the empty squares using the numbers from 1 to the size of the grid (1–9, 1–16 or 1–25). Each number is used exactly once.
- Every row, every column and both long diagonals must add up to the magic sum: 15 on 3 × 3, 34 on 4 × 4 and 65 on 5 × 5.
- The totals are shown above each column, beside each row and in the top-right corner for the two diagonals. They turn green when a full line is right and red if it goes over.
- Tap a square, then a number on the pad. On a keyboard, type the number; for 10 and up, type both digits quickly.
- Each puzzle has exactly one answer, so you can work it out without guessing. Use Hint if you’re stuck.
Magic Square Game skills
- Mental addition
- Number sense
- Logical reasoning
Level: Ages 8 and up
Tips for magic squares
Start with a line that has only one empty square: the missing number is the magic sum minus the others.
In every 3 × 3 magic square, 5 is in the centre and the even numbers sit in the corners.
The magic sum is the total of all the numbers divided by the number of rows: 1 + 2 + … + 9 = 45, and 45 ÷ 3 = 15.
A repeated number turns red, which is a quick way to spot a mistake.
Magic Square Game questions and answers
What is the magic sum of a 3 × 3 magic square?
It’s 15. The numbers 1 to 9 add up to 45, and the three rows share that equally, so each row, column and diagonal adds up to 15.
How do you work out the magic sum?
For a square of size n using 1 to n², the magic sum is n × (n² + 1) ÷ 2. That gives 15 for 3 × 3, 34 for 4 × 4 and 65 for 5 × 5.
How many 3 × 3 magic squares are there?
Just one, if you count rotations and reflections as the same. Turning and flipping it gives eight versions, all with 5 in the centre.
Is this magic square game good for kids?
Yes. Every move is mental addition and subtraction with a clear target, which builds number sense and fluency. The 3 × 3 square suits children from about 8, and the totals light up green so they can check each line themselves.
Can I solve magic squares online?
Yes. You can play magic squares online here for free in three sizes, with a new puzzle each time you press New. Tap a square and pick a number, and the row, column and diagonal totals update as you go.