🧮 Math Cages
Sudoku meets math. No repeats in a row or column, and every cage must make its target.
How to play
- Pick a size and a puzzle. A 3 x 3 uses the numbers 1 to 3, and a 7 x 7 uses 1 to 7.
- Fill the grid so no number repeats in any row or column.
- The thick lines make cages. The numbers in a cage must make its target using its sign: 7+ means they add up to 7.
- A cage with − or ÷ always has two squares, and they can go in either order.
- Tap a square, then tap a number or press it on your keyboard. Notes let you pencil in ideas.
- Clashes turn red, and a full cage that misses its target turns pink.
A free number puzzle like KenKen
Math Cages is a free number logic puzzle for anyone who likes sudoku but wants a bit more math. The rules are simple. Fill the grid with numbers so that nothing repeats in a row or column, and make sure each group of squares, called a cage, reaches its target using the sign shown. It's in the style of KenKen, the popular puzzle invented by Japanese teacher Tetsuya Miyamoto, but all the puzzles here are our own. There are 60 of them, with exactly one solution each, and it takes just a browser to play.
The rules of Math Cages
On an n x n grid, you use the numbers 1 to n. Each number appears exactly once in each row and once in each column, which is the same rule as a Latin square. Thick lines divide the grid into cages, and each cage shows a target and a sign in its top corner. 7+ means the numbers in the cage add up to 7. 2− means the two numbers differ by 2. 12× means they multiply to 12. 3÷ means one of the two numbers divided by the other is 3. A cage with only one square simply tells you the number. Numbers can repeat within a cage, as long as they aren't in the same row or column.
How to solve it
Fill the freebies first. Single-square cages give you a number for free. Look for cages with few options. On a 4 x 4, a 3÷ cage has to be 1 and 3, because no other pair of numbers works. A 7+ with two squares has to be 3 and 4. Use notes. Pencil in both options, even if you don't yet know which way round they go. Use the rows and columns. If two squares in a row hold a pair, no other square in that row can hold those numbers. Add up whole rows. Each row on a 4 x 4 adds up to 10, so if a cage covers most of a row, you can often work out the square that's left over. Try out ideas in your head, then check them against nearby cages.
Five sizes, growing with you
The 3 x 3 puzzles use adding only, so they're great for children who are just getting started. The 4 x 4 puzzles add taking away, and they open at 6 stars. The 5 x 5 puzzles add multiplying at 18 stars, the 6 x 6 puzzles bring all four operations at 36 stars, and the 7 x 7 puzzles open at 60 stars for a real test. Each puzzle earns up to 3 stars: one for solving it, two for solving it with no failed checks, and three for doing that with no hints.
Why it's good for your math
Most math practice gives you a question and asks for an answer. Math Cages turns that around: you know the answer, and you have to find the numbers. That means children end up exploring number facts on their own, trying pairs that make 12 or thinking about factors, and they do it because they want to solve the puzzle. Teachers like this style of puzzle for building number sense and persistence. The KenKen style of puzzle was invented by a teacher for that very reason, to help students learn to think for themselves.
Games like sudoku
If you like sudoku, you'll feel at home here, because the no-repeats rule works the same way. The difference is that the clues are sums and products, not printed numbers, so you need to think about the math as well as the logic. Many people move on to these puzzles when sudoku starts to feel routine. For a more classic number puzzle, try Number Nine on this site, and for the fun of a daily challenge, try Puzzle Numbers.
A worked example
Take a 3 x 3 puzzle, where each row and column holds 1, 2 and 3. Say the top-left cage covers two squares in the top row and says 5+. The only numbers that add up to 5 are 2 and 3, so the third square in that row must be 1. Now look at the cage in the first column. If it's a single square that says 3, then the top-left square can't also be 3, because they share a column. So the top-left is 2, and the next square along is 3. You've just solved three squares by combining the sums with the no-repeats rule, and that's all there is to it. Bigger grids work in just the same way. When you're stuck, look for the cage with the fewest possible combinations, pencil in the options, and let the rows and columns narrow them down. On a 6 x 6, a 3÷ cage could be 1 and 3 or 2 and 6, and it may take a neighbouring cage to tell you which.
More brain games
For more logic, try Logic Grid Detective, Picture Logic or Number Slide. Every puzzle is on the Brain Games page, and there are lots more number games on the Math Games page.
Free and safe
Math Cages is free to play, with no download, no sign-up and nothing to buy. There is no chat, and your progress is saved only on your own device. See the Parents & Safety page for more.
Frequently asked questions
Is Math Cages the same as KenKen?
It uses the same style of rules, but it's our own game with original puzzles. KenKen is a trademark of its owners and has no connection with this site.
Can a number repeat inside a cage?
Yes, as long as the repeated numbers aren't in the same row or column.
Do I have to do the numbers in order for − and ÷?
No. Those cages always have two squares, and the bigger number can go in either one.
Does each puzzle have only one answer?
Yes. We check every puzzle with a solver, so you never need to guess.
What age is it for?
The 3 x 3 puzzles suit children from about seven who can add small numbers. The 5 x 5, 6 x 6 and 7 x 7 puzzles are a good challenge for teens and adults.
Is Math Cages free?
Yes. It is free to play in the browser with no download, no account and nothing to buy.