Magic square: make every line add up
Place the numbers 1 to 9 so that each row, each column and both diagonals add up to 15. The totals around the grid update as you go and turn gold when a line is right. Switch to 4×4 for the harder version, where every line must make 34.
The trick to the 3×3 square
The centre square has to be 5. Every line through the centre pairs two numbers that add to 10 (1 and 9, 2 and 8, 3 and 7, 4 and 6), and only 5 sits in the middle of all four of those pairs. The even numbers then go in the corners and the odd numbers on the edges. There are eight 3×3 magic squares, and they are all rotations and mirror images of one another.
The 4×4 square is much roomier: there are 880 distinct arrangements of 1 to 16 that work. The starting clues here are taken from one valid square, so the puzzle always has an answer.
Sumthread is a calm number-path puzzle: trace one line through every tile and hit the target sums in order. Five-minute boards and a fresh Daily Thread.
Free on the App StoreQuestions
What is a magic square?
A grid of numbers where every row, every column and both main diagonals add up to the same total. With 1 to 9 in a 3×3 grid that total is 15; with 1 to 16 in a 4×4 grid it is 34.
Why is the magic total 15?
The numbers 1 to 9 add up to 45. Three rows share that evenly, so each row must make 45 ÷ 3 = 15. The same reasoning gives 136 ÷ 4 = 34 for the 4×4 square.
Is this good practice for kids?
Yes. It rewards adding small numbers quickly and reasoning about which numbers can go together, and the live line totals show progress without giving the answer away.
Is there an app with puzzles like this?
Sumthread, our iPhone puzzle, uses the same feeling of building exact sums: trace one path through every tile while hitting target totals in order.
- Daily number puzzle for beginners: play today’s SumthreadA daily number puzzle for beginners you can play on this page: one path through every tile, hitting the target sums in order. Scratch to reveal the answer.
- Free number-path puzzle makerMake a new number-path puzzle in one tap: trace one unbroken path through every square so the running total hits each target in order. Print it with or without the answer.
- Grid Path Endpoint Checker: Can a Path Visit Every Square?Pick endpoints on three small grids. Check the alternating color rule, verify whether a complete route exists and reveal a numbered path.