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Puzzles · Calcudoku

Calcudoku: arithmetic that thinks ahead

Calcudoku mixes mental arithmetic with logic: every row and column holds each digit once, and every outlined cage must make its number. This page teaches five ways to find a certain digit and lets you practise with hints that show the reasoning. They never fill in a digit for you.

The rules in one minute

  1. On a board of size n, fill every cell with a digit from 1 to n: 1–4 on a 4×4 board, 1–6 on a 6×6 board.
  2. Each row and each column contains every digit exactly once.
  3. The digits in each outlined cage must make the number in its corner with the sign shown: + adds, × multiplies, − and ÷ take the larger digit first. A cage with only a number holds that number.
  4. A digit may repeat inside a cage, as long as the two cells are not in the same row or column.

Small pencil marks, called candidates, record which digits are still possible in a cell. Cage combinations and Must-contain work on these marks.

The same puzzle is also known as KenKen or Mathdoku.

Practise

The kids' mode uses 4×4 boards with only + and −. In the standard mode, pick a size; hard puzzles need Must-contain.

Keyboard: arrow keys move, 1–4 enters a digit, N switches notes, Backspace erases.

How hints work

Each press of Hint reveals a little more of the same reasoning: first where to look, then the technique's name, then the evidence, and finally a guided walk-through on your own board. You always enter the digit yourself.

Five techniques, one beat at a time

Each lesson plays in five beats: where to look, the evidence, your turn to decide, the conclusion and the rule to remember. Move at your own pace.

  1. 1

    Single-cell cage (Freebie)

    A cage of one cell shows its own digit: write it in.

    1. Look
    2. Evidence
    3. Your turn
    4. Conclusion
    5. Remember

    Look at the cage 1 at row 2, column 2: it has a single cell.

  2. 2

    Line single

    A cell with one candidate left, or a digit with one place left in its row or column, is settled.

    1
    2
    4
    2
    4
    1
    2
    3
    1. Look
    2. Evidence
    3. Your turn
    4. Conclusion
    5. Remember

    Look at row 1: where can 2 go?

  3. 3

    Line total

    A row or column always adds up to the same total. When the cages inside it account for all but one cell, that cell is the difference.

    1
    4
    1. Look
    2. Evidence
    3. Your turn
    4. Conclusion
    5. Remember

    Look at row 4: the cages 6× lie entirely inside it.

  4. 4

    Cage combinations

    List the combinations that make a cage's number, cross out the ones its rows and columns forbid, and keep only the digits that remain.

    5
    1. Look
    2. Evidence
    3. Your turn
    4. Conclusion
    5. Remember

    Look at the cage 7+: which digits can make it?

  5. 5

    Must-contain

    If every combination of a cage puts a digit in one row or column, the other cells of that line cannot hold it.

    3
    1. Look
    2. Evidence
    3. Your turn
    4. Conclusion
    5. Remember

    Look at the cage 8× and row 1.