Calcudoku

How to solve Calcudoku: five moves, no guessing

Updated Tuesday, October 27

To solve a Calcudoku, start with the cages that can be filled only one way, then treat the grid like a sudoku without boxes: every row and column needs each digit once, and each cage's arithmetic cuts the choices down. Every Gridarium calcudoku can be finished this way, without guessing.

The rules

Every row and every column holds the digits 1 to the grid size exactly once, with no boxes. Thick lines split the grid into cages. The corner of a cage shows a target and an operation: its digits add (+), multiply (x), subtract (-) or divide (/) to the target. A cage of one square simply holds its number. Unlike Killer Sudoku, a digit may repeat inside a cage when its squares are not in the same row or column.

Step 1: cages with one answer

Some cages can be filled only one way. A two-square cage marked 3+ holds 1 and 2; on a 4 by 4 grid a 12x cage of two holds 3 and 4, and a 3- cage holds 1 and 4. Write both candidates in as notes: only their order is left to find.

Step 2: work the arithmetic

For each cage, list the sets of digits that make its target with digits up to the grid size. A product narrows things fastest: 10x in two squares is only 2 and 5. The Cage options button lists the sets for the cage you select, taking into account what you have already written: it explains, it never fills a square, and it is free.

Step 3: a digit twice in a cage

An L-shaped cage of three can hold the same digit twice, as long as the two copies are not in the same row or column. So a 4+ cage of three squares on a 4 by 4 grid can be 1, 1, 2 with the ones on the diagonal. Do not rule it out.

Step 4: rows and columns

Once a cage's candidates are narrow, look along its row or column. If a digit can only sit in one square of a row, write it. If every option of a cage puts a 4 in the same row, no other square of that row can be a 4: cross it off, even before the cage is finished.

Step 5: pairs

When two squares of a row can only hold the same two digits, those digits are spoken for: strike them from the rest of the row. The bigger grids need this now and then; the small ones almost never.

The three levels

Easy: 4 by 4, cages of up to 3 squares. Steps 1 and 2 are enough.
Medium: 5 by 5, cages of up to 4 squares. Steps 3 and 4 come into play.
Hard: 6 by 6, cages of up to 5 squares, where step 5 is sometimes needed.