How does Calcudoku work?
Calcudoku is a grid of n × n cells to fill with the numbers 1 to n, each once in every row and every column. The grid is divided into outlined cages. Each cage shows a target and a sign: the numbers in it must make the target with that sign. 12× means they multiply to 12; 3− means two numbers that differ by 3. A cage of one cell simply shows its number.
Choose 4 × 4, 5 × 5 or 6 × 6. Select a cell and tap a number. − and ÷ cages always have two cells and work either way round, so 6 and 2 make 3÷ whichever comes first. A number may repeat inside a cage, as long as the two aren't in the same row or column.
How is your Calcudoku time calculated?
Your result is the time from Start until every cell is filled and nothing breaks a rule. Next to it are the times you pressed Check, which marks any number that disagrees with the answer, and Hint, which fills in one (or fixes a wrong one). A number repeated in a line, or a full cage that misses its target, is outlined in red as you go, worked out from the cages, never from the answer. There is no rating, because no published typical time exists for puzzles built like these.
How do you solve Calcudoku?
- Single cells first. They are already filled in, and each one rules its number out of its row and column.
- Cages with only one pair. In a 6 × 6, 11+ can only be 5 and 6, while 2− has 4 pairs; the table below lists the two-cell targets with a single pair, worked out by the site's code.
- Use the row total. Every row and column of an n × n adds up to n(n + 1) ÷ 2: 10 for 4 × 4, 15 for 5 × 5, 21 for 6 × 6. If a row holds whole cages and one leftover cell, the leftover is the difference.
- Multiplication cages with big primes. A product that 5 divides must contain the 5.
| Sign | Two-cell targets with only one pair (6 × 6) |
|---|---|
| + | 3+: 1 and 2; 4+: 1 and 3; 10+: 4 and 6; 11+: 5 and 6 |
| − | 5−: 1 and 6 |
| × | 2×: 1 and 2; 3×: 1 and 3; 4×: 1 and 4; 5×: 1 and 5; 8×: 2 and 4; 10×: 2 and 5; 15×: 3 and 5; 18×: 3 and 6; 20×: 4 and 5; 24×: 4 and 6; 30×: 5 and 6 |
| ÷ | 4÷: 1 and 4; 5÷: 1 and 5; 6÷: 1 and 6 |
Does every Calcudoku puzzle have exactly one answer?
Yes. Each puzzle is a random Latin square, the filled grid, cut into random cages. It is shown only if a solver that never guesses can finish it: for each cage it lists the ways to fill it that make the target without repeating a number in a line, and it crosses placed numbers out of their rows and columns. The site's tests check hundreds of puzzles of each size and count their answers by trying every possibility: always one.
Is Calcudoku the same as KenKen?
It is the same kind of puzzle. KenKen was invented in 2004 by the Japanese maths teacher Tetsuya Miyamoto, and KenKen and KenDoku are trademarked names, which is why other publishers, and this page, call it Calcudoku or Mathdoku. The rules are the same under every name.
For another puzzle of sums in a grid, try Kakuro; for one where every line adds up the same, the Magic Square.