How to play Kakuro: rules and solving techniques

Kakuro looks intimidating — a grid full of little numbers in triangles — but the rules fit in a paragraph, and once you know three techniques you can solve any puzzle by pure logic. Here's everything you need.

The grid

A Kakuro puzzle is a grid of black and white cells. You write digits only in the white cells. The black cells are either solid, or they carry one or two small clue numbers separated by a diagonal line:

• A number in the upper-right of a black cell is the sum of the white "run" of cells to its right (an across clue).
• A number in the lower-left is the sum of the white run of cells below it (a down clue).

A "run" (also called an entry) is simply the unbroken line of white cells that belongs to one clue — it ends at the next black cell or the edge of the grid.

The two rules

That's the whole game:

1. Each run must add up to its clue. Fill the white cells with digits from 1 to 9 so the run totals the number in the triangle.
2. No digit may repeat within a run. A single across or down run can use each of 1–9 at most once. (Unlike Sudoku, there are no rows, columns, or boxes beyond the runs — only the runs matter.)

Every well-made Kakuro has exactly one solution, and you never have to guess. If you find yourself guessing, there is always a logical step you've missed.

Technique 1: unique sums (the "magic numbers")

This is the heart of Kakuro. For a run of a given length and total, there is often only one possible set of digits. These are worth learning because they give you cells for free. A few of the most useful:

The pattern: the smallest totals for a length force the smallest digits, and the largest totals force the largest digits. A 2-cell run of 17 must be 8 and 9; you don't yet know the order, but you've narrowed two cells to two digits. That's usually enough to get started.

Technique 2: cross-referencing

Every white cell sits at the crossing of one across run and one down run, so it must satisfy both at once. This is where puzzles unravel. Suppose a cell belongs to a 2-cell across run of 17 (so it is 8 or 9) and also to a down run whose only options are {1, 3, 4}. The only digit allowed by both is… none from 8/9 overlaps with 1/3/4 — which tells you your reading of one clue is wrong, or forces the neighbouring cell. More usefully: if the across options are {8, 9} and the down options are {2, 9}, the shared digit must be 9, and the cell is solved.

Technique 3: the leftover

When every cell in a run but one is filled, the last cell is forced: it's the clue minus the digits already placed. It sounds obvious, but combined with the two techniques above it creates a chain reaction — solving one cell completes a run, which forces its last cell, which narrows a crossing run, and so on across the whole grid.

A tiny worked example

Imagine an across clue of 4 over two cells, crossed at its first cell by a down clue of 3 over two cells.

• The across run of 4 (two cells) must be 1 + 3 — the only pair.
• The down run of 3 (two cells) must be 1 + 2 — the only pair.
• The shared corner cell must be in both pairs: {1, 3} and {1, 2}. The only common digit is 1.
• So the corner is 1. The rest of the across run is 4 − 1 = 3; the rest of the down run is 3 − 1 = 2. The whole thing is solved, with no guessing.

Practical tips

• Start where options are fewest — the shortest runs and the most extreme totals (very small or very large), because those have the fewest combinations.
• Pencil in candidates. Write the small set of possible digits in a cell and erase as you eliminate. Our app has pencil marks built in for exactly this.
• Re-check a run whenever you fill one of its cells — a new digit often forces its neighbour immediately.

That's genuinely all there is to it. The rest is practice, and bigger grids are just more of the same chains. If you want unlimited puzzles that are each guaranteed to have one logical solution — plus hints that name the technique to use next — that's exactly what Kakuro by Northcell is built to give you.