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Kakuro

A crossword where the clues are totals and the answers are digits.

Laying out the puzzle…

The rules

The field is made of dark clue squares and white cells. A white run is a line of white cells reading across or down. The number in the clue square to the left of a run (or above it) is the total that run must add up to.

Write a digit from 1 to 9 in every white cell. Digits may not repeat inside a run, so a two-cell run totalling 4 must be 1 and 3, never 2 and 2. Each puzzle has exactly one solution.

Field sizes

Easy fields are 6×6 with runs of up to four cells and can be solved with sum combinations alone. Medium fields are 8×8, hard ones 10×10 and expert ones 11×11, with runs of up to five, six and seven cells. The larger fields may ask you to check whether a whole run can still be completed, not just which digits appear in its possible combinations.

Combinations do most of the work

A handful of totals leave no choice: 3 from two cells is 1+2, 17 from two cells is 8+9, 6 from three cells is 1+2+3, and 30 from four cells is 6+7+8+9. Learn the short list in our sum combinations guide and you will spot them at a glance.

The real power comes from crossings. Every white cell sits where an across run meets a down run, so whatever goes there has to suit both totals at once: compare the two sets of possible digits and keep only what they share. When a 16 in two cells (7 and 9) crosses a run that cannot contain 9, the crossing cell is 7 straight away.

Large totals and small totals are your friends. A long run with a low total is full of small digits; a short run with a high total is full of big ones. Middle totals such as 15 in three cells have many combinations and are best left until their neighbours have narrowed them.

Controls

Tap a white cell and choose a digit from the pad, or type it. Notes work as in sudoku: the pencil button, N, or Shift plus a digit. Duplicates in a run and totals that cannot be reached are highlighted while you play.

Questions

Is kakuro harder than sudoku?

It uses different skills. Sudoku is about placement; kakuro adds arithmetic. Small fields are quick even for beginners, and the 11×11 expert fields are a long, satisfying solve.

Do I need to memorise the combination tables?

No. Knowing a handful of single-combination totals helps a lot, and the guide lists all of them, but you can work every combination out as you go.

What does the hint show?

It marks a cell whose digit follows from the runs crossing it and fills it in. If a digit you entered is wrong, the hint points to that cell first.

Why can't a run repeat a digit?

That is the defining rule of kakuro. Without it most totals would have many more combinations and the puzzles would lose their single solution.