Calcudoku

Read a cage as a set of possibilities

Suppose a two-cell cage says 7+ on a 4 × 4 board. The available digits are 1, 2, 3 and 4, so the only pair that adds to seven is 3 and 4. You still need to decide which cell receives 3. Row and column clues elsewhere can settle the order. A 6× cage could contain 2 and 3, while an 8× cage could contain 2 and 4. A subtraction or division target may also have a small set of possible pairs. List those pairs before entering a number, then use the grid to remove impossible arrangements.

The side length matters. A pair that would work with 5 is irrelevant on a 4 × 4 board, because 5 is not an allowed digit. If the board size changes, recompute the candidates for that size rather than memorising a fixed pair. A target of 5+ might mean 1 and 4 or 2 and 3 on a 4 × 4 grid. Both are arithmetically correct; only the intersecting rows and columns will tell you which fits a particular cage.

Let a given cell start the chain

The publisher recommends filling single-cell cages first. They require no pair calculation: if a one-cell cage shows 2, enter 2. Then inspect its row and column. Neither can use another 2. Now look at any neighbouring two-cell cage. If one of its possible pairs needs a 2 in that row or column, that arrangement is ruled out. The given value can therefore resolve a cage several cells away through the row or column restriction.

For a useful example, imagine a 4 × 4 row already contains 1 and 4. The two empty cells must contain 2 and 3, in some order. If one empty cell belongs to a 3÷ cage, it cannot be 2 or 3 paired with a valid neighbour to make a quotient of three unless the partner is 1 and the arrangement fits. If that partner is excluded by its column, the cell is forced. The exact deduction depends on the board, but the method is stable: list missing row digits, compare with cage pairs, then check columns.

Addition, subtraction, multiplication and division cages

Each printed operation asks a different question. An addition target gives a sum; a multiplication target gives a product. For subtraction, think about the difference between the two cage values. For division, think about their quotient. On a 4 × 4 board, a 2÷ cage might use 1 and 2 or 2 and 4, if row and column positions permit. Do not assume the larger value appears first on the board; the pair must satisfy the operation regardless of reading direction unless the game explicitly states otherwise. The on-screen clue is the authority for a particular puzzle.

Multiplication pairs can be especially efficient. A 12× cage on a 4 × 4 board must use 3 and 4. A 4× cage could use 1 and 4 or 2 and 2, but two equal 2s cannot share a row or column under the no-repeat rule. If the cage cells lie in the same row or column, that removes 2 and 2 immediately. This is why arithmetic and grid position must be considered together. A pair may be mathematically correct while still impossible in the puzzle.

Keep candidates until they are forced

Entering the first plausible number can create a chain of later mistakes. If a cage can be 1+4 or 2+3, record both possibilities mentally or in notes rather than choosing one by appearance. Check the row's missing digits and the column's missing digits for each cell. A candidate survives only if it is allowed by all three constraints: its row, its column and its cage. When one candidate disappears, the remaining value becomes a justified move.

After every entry, scan the entire row and column before moving on. A digit placed in one cell may be the missing piece for several others. If a duplicate appears, correct it immediately. The goal is not to fill as many cells as possible; it is to reduce uncertainty without violating the rules. Practice undo is useful for revisiting a tentative choice, but an explicit candidate list is often more efficient than entering and erasing guesses.

What makes this different from Sudoku?

Ordinary Sudoku adds box constraints to rows and columns. Calcudoku uses arithmetic cages instead. A row can look nearly complete, but a cage may still reveal that the remaining pair is in the wrong order. Shikaku is another grid puzzle if you enjoy working from constraints. Logic Puzzles includes Calcudoku because deduction from intersecting rules is its central activity. Kakuro Mini is another arithmetic grid, but its sums run along entries rather than one- or two-cell cages. The puzzles share number sense without sharing identical rules.

The publisher offers a daily board and Practice difficulty. A daily solve has a move-based score and leaderboard conditions; guest play and Practice do not require chasing that ranking. Try a small Practice board first. Work out each cage's possible values, then fill single-cell givens and apply row and column exclusions. Once you can explain your first few entries, a new daily board provides a fresh mix of the same rules.

Four short checks before entering a digit

Is the digit within 1–N? A 4 × 4 grid does not allow 5, even if a target could be reached with it.

Will it repeat in its row or column? Every digit appears once in each.

Can its cage still reach the target? Recalculate with the companion cell and the printed operation.

Is another candidate still possible? If yes, keep both until a row, column or neighbouring cage rules one out.

Calcudoku rewards the moment when three separate clues agree. An arithmetic pair suggests values, the row narrows them, and the column decides where they belong. Solve each small cage in the context of the whole board, and the grid becomes a chain of deductions rather than a page of guesses.

How to play Calcudoku

Choose Practice. Fill each row and column with 1–N exactly once. Use each cage's operation and target to narrow possible values before entering them.

Controls: Select a cell and enter a digit. Use Undo in Practice to revise a move.