Puzzle guide
How to solve Calcudoku
Calcudoku mixes a number grid with small sums. Every row and column holds each number once, and thick lines split the grid into cages, each with a little sum in its corner. You do not need to be fast at maths: a few tricks do most of the work.
The rules
- Fill every cell with a number from 1 up to the size of the puzzle: 1 to 4 on a 4×4 puzzle, 1 to 6 on a 6×6.
- Every number appears exactly once in each row and each column.
- Thick lines make cages. The numbers in a cage give the small number in its corner by the operation shown: 8+ means they add up to 8, 12× means they multiply to 12.
- For − and ÷, start with the bigger number: 2− means one number is 2 more than the other, 2÷ means one is twice the other. These cages always have two cells.
A solved puzzle
Your first moves
- Fill in cages of one cell: their number is already given.
- Look for cages with only one way to reach their target, like 3+ in two cells (1 and 2) or 12× in two cells on a 4×4 puzzle (3 and 4).
- Remember that a full row adds up to the same total every time: 10 on a 4×4 puzzle, 21 on a 6×6.
- Write notes for the numbers a cell can still hold, and update them when a row or column fills.
Techniques, step by step
The last number in a row
This row already holds 3, 1 and 2. Every number appears once in a row, so the last cell is the missing one: 4. The same works for columns, and for a cell whose row and column together use every other number.
Cages with only one way
On a 4×4 puzzle, a 3+ cage of two cells can only be 1 + 2, and a 12× cage of two cells can only be 3 × 4. You do not know the order yet, but you know which two numbers go there. Small and large targets are the best start: 3+, 7+, 12× and 3− (always 4 and 1) all have just one pair.
What is left of a row
A row of a 4×4 puzzle always adds up to 1 + 2 + 3 + 4 = 10. Here an 8+ cage covers three cells of the coloured row. So the fourth cell is 10 − 8 = 2. On bigger puzzles the total is larger (21 on 6×6, 45 on 9×9), but the trick is the same: subtract the cages that lie completely inside the row.
Only one place for a number
Where can the 3 go in the top row? The second and third cells already have a 3 below them in their columns, and the first cell is taken. Only the last cell is left, so the 3 goes there. Asking where a number can go is often faster than asking what a cell can hold.
Try every way to fill a cage
For a bigger cage, list every set of numbers that hits its target and still fits the row and column rules. A number that none of them uses can be crossed out of the cage. For example, on a 4×4 puzzle 2÷ in two cells is 1 and 2, or 2 and 4: either way one of the two cells is a 2, and a 3 never fits. This is the technique Calcudoku is really about.
A cage that locks its row
The 7+ cage lies in one row and must hold 3 and 4. Those two numbers are then used up for the whole row. So the other cells of the row can only be 1 or 2. Whenever every way of filling a cage puts a number in the same row or column, cross it out of the rest of that row or column.
Common mistakes
- Repeating a number inside a cage that spans two rows. Repeats are only forbidden within one row or column. An L-shaped cage may hold the same number twice if they are in different rows and columns.
- Subtracting the wrong way round. For − and ÷, take the bigger number first. 2− with a 1 means the other cell is 3.
- Forgetting the order does not matter. 6× in two cells could be 2 × 3 or 3 × 2; check the row and column to decide.
- Old notes. After placing a number, remove it from the notes in its row and column.
Questions and answers
Ready to play?
Single cages, cages with only one way, the total of a row and cages that lock their row: with these, every Calcudoku comes apart cage by cage.