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 7 on a 4×4 grid must be {3, 4} (2+5 and 1+6 need digits above 4, so 3+4 = 7 is the only pair). 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 6×6 grid the digits are 1–6, not 1–9. A multiplication cage of '10×' on a 6×6 must be {2, 5} or {1, 10} — but 10 is out of range, so it can only be {2, 5}. 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 two candidate pairs ({1,3} and {2,6}). 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.

CAGE LOOKUP

Pick the board, how many cells your cage covers, the operator and the number printed in it. Every way to fill that cage appears below, with the digits that must be in it and the digits that cannot. Most cages on a GridJoy board are three or four cells — the sizes worth looking up, because nobody enumerates 144× over four cells in their head.

LOCKED 2-CELL CAGE REFERENCE

A locked cage is a two-cell cage whose clue leaves exactly one possible pair of digits — a deduction you can make before looking at a single row or column. The digits in a two-cell cage always share a row or a column, so they can never be the same.

Which clues are locked depends on the board: a 4×4 has thirteen, a 7×7 has twenty-six. GridJoy deals one size per tier, 4×4 up to 7×7, so all four are here.

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.