Calcudoku looks like a small Sudoku but runs on arithmetic. Every row and column must contain the digits 1 up to the size of the grid, once each. On top of that sit cages — the thickly outlined regions — and each cage carries a target and an operator. A cage marked 6× means its digits multiply to 6. The same puzzle is published elsewhere under the name KenKen.
How to solve it
Take the single-cell cages first. They are free: the target is the digit. Each one also strikes that digit from its row and column, which often opens up the neighbours.
Move on to two-cell cages with subtraction or division, because they carry the fewest possibilities. In a five-grid, 4− can only be the pair 1 and 5. Order does not matter — it is always the larger number minus the smaller.
Multiplication is deceptively useful. A target like 15 in a five-grid can only come from 3 and 5, because no other permitted digits build it. Primes and large targets are your best clues.
Do not lose sight of the whole: every row sums to the same total. In a five-grid that total is 15, since 1+2+3+4+5 is 15. Once you know what the cages in a row account for, the remainder is arithmetic.
What makes a puzzle hard
Grid size and cage shape together. Large cages with addition or multiplication admit many combinations and give away little early, while small cages pin digits down immediately. A hard puzzle has fewer single-cell gifts and more sprawling cages.
A worked example
In a five-grid you meet a two-cell cage marked 2÷. A quotient of two can only come from the pairs 1 and 2, 2 and 4, or 3 and 6 — but no six exists in a five-grid, so two pairs remain. If the cage sits in a row that already holds a two, the answer is settled.
The most common mistake
Treating subtraction and division as directional. Inside a cage, 3− means the difference between the digits is 3, not that one particular cell is subtracted from another. The same goes for division: it is the larger digit divided by the smaller.