Cages – a 4 × 4 number puzzle
Fill in the digits from 1 to 4 so that they don’t repeat in any row or column, and the numbers in each cage give the result in its corner.
Does every cage add up?
How do you play Cages?
The grid has 4 rows and 4 columns. In each row and each column write the digits 1, 2, 3 and 4 – each exactly once. Thick lines split the grid into cages. In the corner of a cage there is a result and an operation sign, for example 7+ or 2÷. The numbers in the cage must give that result: in a 7+ cage the numbers add up to 7, in a 1− cage the difference of the two numbers is 1 (take the smaller from the larger), and in a 2÷ cage the larger number divided by the smaller gives 2. In Polish exercise books division is written with a colon (:). A cage with one square and just a number gives you the digit.
A digit may appear twice in a cage if those squares are not in the same row or column. Every puzzle has exactly one solution.
Where do you start?
One-square cages. Write the given digit straight away. Cages where only one pair fits. A two-square 7+ cage can only hold 3 and 4, and a 3− cage only 1 and 4. Rows and columns. If a row already has 1, 2 and 4, the last square must be 3. The four numbers in each row always add up to 1 + 2 + 3 + 4 = 10.
What is the most common mistake?
Subtracting in the wrong order. In a 1− cage with 2 and 3 the result is 3 − 2 = 1, not 2 − 3. Always take the smaller number from the larger, and when dividing, divide the larger by the smaller.
How does this help in the eighth-grade exam?
Cages practise splitting a number into factors: if a two-square cage has the result 12 and a multiplication sign, it can only hold 3 and 4. The same skill is needed in the Polish eighth-grade exam when simplifying fractions and working out roots – for example √36 = 6, because 36 = 6 · 6. In 2025, question 7 with roots and fractions was answered correctly by only 37% of pupils.
Curriculum: points II.1, II.3 and II.4 for grades 4–6 (Polish core curriculum, Dz.U. 2024 poz. 996). Source: CKE report 2025 (in Polish).
Questions about the game
How is Cages different from ordinary sudoku?
In ordinary sudoku only repeated digits matter. Cages adds operations: the digits in each cage must give the result in its corner.
Who is this puzzle for?
For pupils in grades 4–8 and for anyone who wants to practise mental maths. The easy level is enough to start.
Is the game free?
Yes. You play in the browser, with no sign-up and no e-mail.
Mini glossary: English – Polish
- row – wiersz
- column – kolumna
- cage (group of squares) – klatka
- addition – dodawanie
- subtraction – odejmowanie
- multiplication – mnożenie
- division – dzielenie
The game runs in your browser. No time limit. We send nothing – only your browser remembers your progress on the puzzle of the day.