How to play Calcudoku

Small arithmetic clues, one satisfying Latin square. Start with the fixed digits, then combine row, column and cage reasoning.

Play Calcudoku

These original teaching diagrams are separate from your saved board. Switch back to its tab to preserve Undo history.

Rows, columns and cages

On a 4 × 4 board use 1–4 once per row and column; on 5 × 5 use 1–5, and on 6 × 6 use 1–6. There are no Sudoku boxes. Every cell belongs to one connected bold cage, whose top-left label gives a target and operation.

+: all cage digits add to the target.
×: all cage digits multiply to the target.
−: two cells, larger minus smaller.
÷: two cells, larger divided exactly by smaller. No fractions or rounding.
A one-cell cage has no operation: its target is a fixed given.

Order does not matter for subtraction or division. A 2÷ cage on a 4 × 4 board may contain 1 and 2, or 2 and 4. It does not prescribe which cell is larger.

A cage is not an all-different region. Equal digits are allowed in the same cage when they are in different rows and columns. For example an L-shaped 6+ cage may contain 1, 4, 1, with the two 1s on different rows and columns. Only a common row or column forbids repetition.

An original four-by-four lesson

Letters below identify cages, not values. Each pair in the first two rows is one cage; every digit in the bottom two rows is its own fixed singleton. A: 3+, B: 1−, C: 6×, D: 4÷.

A	A	B	B
C	C	D	D
3	4	1	2
4	1	2	3

Column 1 is missing 1 and 2; column 2 is missing 2 and 3. Cage A sums to 3, so its pair must be 1 and 2. Column 2 cannot take 1: enter 2 at row 1 column 2, then 1 at row 1 column 1.
Columns 1 and 2 now each have one space: row 2 starts 2, 3. Their product is 6, matching cage C.
Cage D divides to 4. In the range 1–4 its only pair is 4 and 1. Column 3 already contains 1 and 2, so row 2 column 3 is 4, and row 2 column 4 is 1.
Column 3 now needs 3 at row 1. Row 1 needs 4 in its last cell. Cage B checks out: 4 − 3 = 1.

1	2	3	4
2	3	4	1
3	4	1	2
4	1	2	3

Check every row, column and cage, rather than accepting a plausible-looking total. This original lesson is not a production generation fixture.

The five checked engine rules

Only one candidate

A fixed digit or checked singleton rules that digit out of every other cell in its row and column. A cage is not an all-different group: do not remove a digit merely because it appears elsewhere in the cage.

Only one place in a line

A row or column must contain every digit once. If a digit has only one supported location after all preceding checked deductions, keep it there and remove the cell’s other candidates.

Original cage combinations

Enumerate combinations meeting this cage’s operation and target using the full digit range except fixed or currently singleton cells. Enforce repeats only when cage cells share a row or column. Remove digits with no supporting combination.

Cage combinations with current candidates

Use all candidates remaining after preceding checked deductions. Retain every cage tuple that meets the arithmetic and internal row/column constraints; remove a digit only when no tuple supports it. Your pencil notes never restrict this enumeration.

Complete row or column arrangements

Enumerate all one-of-each arrangements compatible with the current checked candidates in this row or column. A candidate absent from every complete arrangement can be removed. This is stronger than checking each digit separately.

Read a hint’s deductions in order. Later steps can depend on candidates removed earlier. Easy uses peer singles, hidden singles and static cage combinations. Medium adds current-domain cage support; Hard adds unit matching. These are technical repertoires, not promises of human difficulty. New currently offers 4/5/6 Easy and 6 Medium only; Reopen does not depend on this gate.

Input, notes and checked hints

Select a cell and use the number pad or 1–N. Arrow keys move selection; N toggles notes; Delete or Backspace erases. Hold a pad number to inspect matching values, or Shift plus a number to lock its highlight. Space enters that number or toggles its note. Undo and Redo change one ordinary move at a time.

Singleton cages cannot be edited. Notes are possibilities, never premises for deductions. Automatic cleanup removes the placed digit from notes in its row and column only, never from the rest of its cage. Turn cleanup off in settings if preferred.

Check marks incorrect entries without changing them. Hints can place one forced digit or remove one existing note, and show the checked chain that justifies it. Apply is available only for the exact unchanged board and session. Editing, Undo, Redo, restarting, navigating or canceling invalidates it. A recheck or stalled hint never reveals an answer.

Pause stops entry and the clock. Relaxed mode has no mistake limit; challenge mode ends at three mistakes and can continue relaxed. New and imports verify before replacing play; cancel or failure keeps your board and saved bytes. Download progress before deliberately replacing a conflicting saved copy. Shared links carry only the clean puzzle code, not entries, notes or timer.

Print the original cages

Use Print board beside the player. The default sheet contains original cages and singleton givens only. Current entries and notes are separate opt-ins. Preview captures a copy of that board and snapshot; closing or canceling printing does not edit, pause or rewind play.

Choose portrait A4 or US Letter, 100% scale, with browser headers and footers off. The sheet uses dark outlines on white paper and works without printed backgrounds. Solve with pencil, or use the sheet to explain a deduction to someone else. Printing never includes the admitted answer or certificate.

Daily puzzles and recovery

Daily Calcudoku and the published archive use real immutable publications. An unpublished date stays unavailable; visiting it never generates a substitute. Completing an ordinary code is not proof it was a daily puzzle.

Progress stays in this browser, separated by game and exact code. Home lists saved boards; opening them requires native verification. Keep downloads for another device. Optional local activity is off until you enable it and counts deliberate play, not imports or history replay.