Calcudoku Puzzles

Common questions

How do you play Calcudoku?

Fill an N × N board so every row and every column holds each digit from 1 to N exactly once. The board is split into outlined cages, and the label in each cage's corner gives a target and an operation: + means the digits add up to the target, × means they multiply to it, − means the larger minus the smaller equals it, and ÷ means the larger divided by the smaller equals it. Subtraction and division cages always have exactly two cells and can be read in either order, so a 2÷ cage accepts 2 and 4 either way round. A cage with one cell shows the digit that goes in it. Digits may repeat inside a cage when they sit in different rows and columns. A three-cell 6+ cage in one row accepts 1, 2 and 3; 2, 2 and 2 also add up to 6, but the row then repeats 2, so the board flags it.

Can I choose the board size and operations?

Yes. Boards come in 4 × 4, 5 × 5 and 6 × 6, and four checkboxes choose addition, subtraction, multiplication and division. Keep addition or multiplication selected, because cages of three or four cells need one of them. The generator uses only the operations you select: subtraction and division appear only on two-cell cages, and division only where the larger digit is a whole multiple of the smaller. The same size, operations and seed always build the same puzzle.

Does every puzzle have exactly one solution?

Yes. For each seed the generator fills a random Latin square, splits the board into joined cages of one to four cells and gives each cage an allowed operation that its digits make. A fast solver screens the candidate, and then a separate solver that fills the board cage by cage, without knowing the intended answer, must prove exactly one solution within 300,000 steps before the puzzle is offered. The page repeats that proof when the puzzle opens. A candidate whose cages allow two solutions is discarded, and a proof that reaches its step limit offers nothing; each seed may try up to 64 candidates within 2,000,000 steps. If a seed fails, Generate from seed keeps the previous puzzle and New puzzle moves on to another seed. Steps are counted, not timed, so the same seed builds the same puzzle on every device.

How do pencil notes, hints and undo work?

Turn on Pencil notes, or press N, to mark candidate digits in a blank cell. Notes never count as submissions, and entering a digit replaces them. Hint writes the correct digit into the selected cell when it is blank or wrong, otherwise into the first blank or wrong cell, and turns the run into assisted practice. Reveal solution shows the answer while keeping your own entries underneath. Undo and redo step through digit and note changes until the puzzle is solved; once every rule holds the result is final, and Replay as practice starts the same puzzle again.

How is the Calcudoku challenge scored?

The challenge is one seeded original 4 × 4 puzzle that may use all four operations. Score is 1000 minus your final retained digit submissions, never below 0, and higher is better. Every one of the 16 cells, single-cell cages included, needs at least one submission, so 984 is the best possible score. A submission is a digit you enter that changes a cell, including a digit that replaces another. Pencil notes, erasing a cell and entering the digit a cell already holds add nothing. Undo takes back the submission it undoes and redo counts it again, until the puzzle is solved. Hint, Reveal solution, an answer key printed before finishing, restored progress, replays and puzzles already opened in this browser, including rotated or reflected copies, stay practice. A scored result stays on the page until you earn a newer one, even when you replay the puzzle or start another. Scores are self-reported.

What happens when someone opens a challenge link?

The page shows the shared score, the fixed rules and a Start same challenge button; nothing starts on its own. The link carries only the seed, the board size setting and the claimed score, never digits, notes or the answer, and the board is regenerated from the seed with all four operations. The button starts one attempt per visit, and a puzzle already opened in this browser stays practice. A challenge link with a fractional, out-of-range, duplicated or wrong-tool value is refused with a message, and ordinary practice opens instead. After a fresh unassisted solve you see both scores, the signed difference and whether you did better, tied or scored lower, with Copy challenge link, Share challenge and Download result card for a new link that carries your score for the same puzzle.

Can I print a puzzle or come back to it later?

Print puzzle prints the cages and targets only, without your entries, notes or the solution. Print puzzle and answer key adds the answer on a separate page and, if you have not finished, turns the run into assisted practice. The printable copy leaves the page once the print dialog closes. Your size, operations and seed are saved in this browser, and once you make a change the puzzle's progress is saved too, without the solution. On your next visit an unfinished puzzle reopens automatically, unless you arrive through a challenge link: it is regenerated from its seed and your history is replayed onto it, as practice. Every puzzle that opens is remembered straight away, up to 1,024 of them, so reloading never turns a puzzle you have already seen into a fresh attempt. Saves keep up to 10,000 changes. If storage is unavailable, the puzzle stays playable in the open tab, but nothing is remembered after you leave.

Can I play with a keyboard or on a phone?

Yes. Tap a cell or use the arrow keys, then press a digit key from 1 up to the board size to enter it, Backspace or Delete to clear, and the N key to switch pencil notes. The digit pad, the Left, Up, Down and Right buttons and a selected-cell list give the same control without a keyboard, and on narrow screens every cell and button is at least 44 pixels. Each cell's accessible name includes its digit, its notes and its cage's target and operation, and the page lists every cage as made, open or no longer possible, plus a text version of the board.