Calcudoku · strategies

Cages are constraints.

Every cage restricts its cells to a short list of digit combinations. Cross-reference those with the Latin-square rule and most cells fall without guessing.

Single-cell cages

A cage marked with just a number and no operation is a single cell — its value IS the target. Place it immediately; these are free givens that anchor the grid.

A 4×4 cage of one cell marked “2” has no operator — the digit is simply 2. Ring it and move on.

Small division and subtraction cages

Division and subtraction in a 2-cell cage have very few valid digit pairs. In a 4x4, a subtraction cage with target 3 can only be (4,1). Pin those pairs early — even without knowing their order, they eliminate digits from the row/column.

A 2-cell 3− cage in a 4×4. The only pair with difference 3 is {4,1} — order unknown, but 4 and 1 are now barred from the rest of that row and column.

Addition cages as sum constraints

A 3-cell addition cage in a 5x5 with target 6 must contain digits 1+2+3 — the only triple summing to 6 with digits 1 through 5. Knowing the SET (even without positions) eliminates those digits from the rest of their rows and columns.

A 3-cell 6+ cage in a 5×5. Digits 1–5 give only one triple summing to 6: {1,2,3}. The set is locked even before the positions are.

Row and column pencil-marking

Once you know a cage’s possible digit sets, note candidates in each cell. The Latin rule eliminates: if 3 is placed in row 2, no other cell in row 2 can hold 3 — even across cage boundaries.

Order of attack

Singles first, then small division/subtraction cages, then enumerate addition and multiplication sets, then row/column elimination. Repeat until solved — our puzzles never require guessing.

Try today’s puzzle →

← Calcudoku category