Calcudoku: rules, strategy, and free play

THE RULES

1. Fill every cell with a digit from 1 to N (where N is the grid size — 1–4 on a 4×4 grid, 1–7 on a 7×7).
2. Each row and column must contain every digit exactly once. Same constraint as Sudoku, minus the 3×3 box rule.
3. Each cage (outlined region) must produce its target. The number + operator in a cage's corner shows the target and the operation. For + and ×, the order of the digits doesn't matter. For − and ÷, the operation is applied between the two largest digits in the cage (cages with − or ÷ are always exactly 2 cells).
4. Digits CAN repeat within a cage. Unlike Kakuro, a 3-cell sum-cage of 7 could be 1+1+5 or 2+2+3 — as long as the row/column rule isn't violated.

BEGINNER STRATEGY

• Solve the singletons first. A 1-cell cage shows the digit directly (e.g. '3' in a 1-cell cage means that cell is 3). Place these immediately; they constrain everything around them.
• Use cage math to narrow rows. A 2-cell × cage with target 6 on a 4×4 grid must be {2, 3} (1×6 is out of range, 2×3 = 6). That tells you which two digits live in those two cells before you've even checked the row/column.
• Subtraction cages reveal pairs fast. A 2-cell − cage with target 3 on a 5×5 grid can only be {1,4} or {2,5} — eliminate the pair where neither digit fits the row/column.
• Cross-reference cage candidates with row/column elimination. A cage's possible digit sets intersect with the row/column's remaining digits. The overlap is usually one or two valid placements — much tighter than working either constraint alone.
• Never guess. Every legitimate Calcudoku has a unique solution found by deduction. If you find yourself guessing, look for a cage you haven't fully expanded.

COMMON MISTAKES

• Confusing Calcudoku with Killer Sudoku. Calcudoku has no 3×3 box rule, cages use all four operators, and digits CAN repeat within a cage (if the row/column allows it). These three differences change the feel completely — don't import Killer Sudoku habits.
• Ignoring the grid-size digit ceiling. On a 5×5 grid the digits are 1–5, not 1–9. A multiplication cage of '12×' on a 5×5 must be {3, 4} or {2, 6} — but 6 is out of range, so it can only be {3, 4}. Always check the grid size before evaluating cage possibilities.
• Treating subtraction/division cages as flexible. Subtraction and division cages are always exactly 2 cells. The result is |a − b| or max(a,b) ÷ min(a,b). Both cells must be distinct and in range — there are often very few pairs. Evaluate these first.
• Forgetting the no-repeat row/column rule after placing a cage. Once you know a cage contains {2, 3}, those two digits are 'used up' in any row or column that cage spans. Eliminate them from other cells in those rows/columns immediately.

HOW TO THINK ABOUT IT

Calcudoku lives between Sudoku (pure elimination) and arithmetic (pure calculation). The best approach is to enumerate cage candidates first, then cross-reference with row/column elimination, then re-evaluate cages with the updated candidates. One pass is rarely enough — each layer of elimination feeds the next. Work in rounds, not in one linear sweep.

WHY THIS PUZZLE REWARDS YOU

Calcudoku is GridJoy's go-to puzzle for players who like Sudoku but want a maths layer on top. Where Sudoku is pure constraint-satisfaction, Calcudoku rewards numerical intuition: recognising that 24 = 2×3×4 OR 1×4×6 on a 6×6 grid, that a cage of '15+' in 3 cells limits the digit set to ≥ {4,5,6}, that a 2-cell '/' cage on a 7×7 with target 3 has exactly four candidate pairs. KenKen was invented in 2004 by Japanese maths teacher Tetsuya Miyamoto specifically as a brain-training puzzle — it's still one of the most analytically demanding number puzzles available.

LOCKED 2-CELL CAGE REFERENCE (6×6)

On a 6×6 grid (digits 1–6), the clues below have exactly one valid digit pair — a forced deduction requiring no row or column context. Scale accordingly for 4×4 (digits 1–4) and 5×5 (digits 1–5): the extremes shift, but the pattern (minimum/maximum combinations collapse to a single pair) holds at every size.

VARIANTS

• Killer Sudoku. Sum-only cages plus Sudoku's 3×3 box rule. Digits cannot repeat within a cage. Closer to Kakuro in feel — no multiplication or division.
• Kakuro. Sum-only cages in a crossword grid. No row/column uniqueness constraint beyond the cage no-repeat rule.
• Skyscraper. Latin-square base like Calcudoku, but constraints come from edge visibility clues rather than arithmetic cages.

YOU MIGHT ALSO LIKE

• Killer Sudoku →

  Cage sums on a Sudoku base — different operator, same spirit.

• Kakuro →

  Sum-only cages with the no-repeat-within-run rule.

• Sudoku →

  The classic Latin-square puzzle Calcudoku builds on.

• Skyscraper →

  Latin square + edge-visibility constraints instead of cages.

• Countdown →

  Six numbers, four operations, one target — pure mental arithmetic.

• How to play Calcudoku (visual guide) →

  New to it? A cage's target hands you its digits — a real 4×4 solved in pictures.