How to play Calcudoku
Calcudoku is a Latin-square logic puzzle with arithmetic. Fill the grid so that every row and every column contains each digit from 1 up to the grid size exactly once.
The grid is also divided into cages with bold ink walls. The digits in each cage must make the target in its corner using the operation shown.
Rules
- A 4 × 4 grid uses 1–4, a 6 × 6 uses 1–6 and a 9 × 9 uses 1–9. No digit repeats in a row or a column.
- + means the cage adds up to the target and × means it multiplies to it. − and ÷ cages always have two cells: take the smaller digit from (or divide it into) the larger one.
- A cage with just a number and no sign is a single cell: that digit is given to you.
- A digit may repeat inside a cage, as long as the two copies aren’t in the same row or column.
- Clashing digits are highlighted, a full cage that misses its target is underlined, and a correct cage fades its label. A hint fills in one correct digit, but hinted solves don’t count towards your best time.
Controls
- Click / tap a cell
- Select it, then pick a number on the pad (or drag a number onto a cell)
- 1–9
- Place a digit (Shift + digit adds a note)
- Arrows / WASD
- Move the selection
- N
- Toggle notes mode
- M
- Toggle auto notes (off clears all notes)
- Backspace / 0
- Erase
- Z / Ctrl+Z
- Undo
- H
- Hint
- P
- Pause
Tips
- Fill in the single-cell cages first, then strike those digits from their rows and columns.
- Big and small targets have few ways to be made: 3+ in two cells is 1 and 2, and on a 6 × 6 a 30× pair can only be 5 and 6.
- Each row adds up to the same total (10 on a 4 × 4, 21 on a 6 × 6, 45 on a 9 × 9). When a row is covered by whole cages plus one stray cell, subtraction gives you that cell.
Calcudoku strategy
Read the extremes of − and ÷
Some two-cell clues have only one pair. On 6 × 6, a 5− cage is always 1 and 6. On 9 × 9, an 8− cage is 1 and 9, and a 9÷ cage is 1 and 9 as well. Nearby targets are nearly as tight: on 6 × 6, 3÷ is 1 3 or 2 6, and on 9 × 9, 4÷ is 1 4 or 2 8. A 1− cage, by contrast, tells you almost nothing.
Factor the × cages
Break a × target into primes. Only a 5 supplies a factor of 5, and on 9 × 9 only a 7 supplies a factor of 7. So a cage whose target divides by 5 must hold a 5, and one that divides by 25 must hold two 5s, which then sit in different rows and columns. Big two-cell targets are tight too: on 9 × 9, 72× is 8 and 9, and 63× is 7 and 9.
Let pairs claim their line
When a two-cell cage lies within one row and its digits are fixed as a set, say 1 and 6 from 5−, those two digits are used in that row. Strike them from every other cell in it. Two such cages in one row on a 6 × 6 leave only two digits for the last two cells. The same works down columns, and it is often quicker than any sum.
Rows multiply too
Each row’s digits multiply to the same total: 24 on a 4 × 4, 720 on a 6 × 6 and 362,880 on a 9 × 9. When a row is covered by whole × cages plus one stray cell, divide to find it. Auto notes help with cage and row clashes, but they are recomputed after every digit you place. Any digit you strike by hand will reappear, so make those deductions in your head.
About Calcudoku
The puzzle was invented in 2004 by Tetsuya Miyamoto, a Japanese maths teacher who wanted his pupils to practise arithmetic and logic at the same time. It spread through newspapers worldwide a few years later under several brand names; Calcudoku and MathDoku are the generic ones.
Every puzzle here is generated fresh: a random Latin square is cut into cages of one to four cells and each cage gets an operation. A solver then checks the result has exactly one solution and re-cuts any cages that leave room for a second. We added pencil notes, auto notes, hints, undo and a saved game for each size.
Questions
What do the symbols in the cages mean?
+ is a sum, × a product, − the difference between two digits and ÷ the larger digit divided by the smaller. A number with no sign is a single cell whose digit is given.
Can a number repeat inside a cage?
Yes, if the two cells are in different rows and columns. A 3-cell L-shaped cage can hold, say, 2, 1 and 2.
Does every Calcudoku have one solution?
Yes. Each generated puzzle is checked by a solver, and cages are re-cut until only one filling of the grid fits every cage.
Which size should I start with?
The 4 × 4 is a two-minute warm-up that teaches the rules. The 6 × 6 is a coffee-break puzzle, and the 9 × 9 is a proper session with plenty of multiplication.