What Are the Key Kakuro Rules for Sums, Runs, and No Repeats?

Kakuro is a number crossword: fill every white cell with a digit from 1 to 9 so that each across run matches its clue sum, each down run matches its clue sum, and no digit repeats inside a single run. The three rules to internalize are clue direction (lower-left triangle = across, upper-right = down), sum matching, and no repeats within a run — digits may repeat elsewhere on the board as long as they belong to different runs. On kakuro-puzzle.online you enter digits directly on the board with the number pad; there are no equations to type and no words to submit.

Rule 1: Read the clue direction correctly

Each black clue cell can hold one or two numbers, and their position tells you which run they control.

To trace a run, start at the black clue cell and follow the connected white cells until another black cell or the board edge stops you. That straight line is the only group the clue governs — a clue never applies to a whole row or column beyond its own run.

Rule 2: Match the sum exactly, using 1–9 only

Every white cell takes a single digit from 1 through 9. The digits in a run must add up to the clue number exactly. The site's own walkthrough makes the constraint concrete: a two-cell clue of 3 must be 1+2 (in either order), because 2+2 would repeat a digit and 3 alone would need a third cell.

The same logic rules out the most common beginner error: a two-cell clue of 4 is 1+3, never 2+2. If you catch yourself writing a pair of identical digits to hit a sum, the entry is wrong by definition.

Rule 3: No repeats inside a run — but repeats across runs are fine

The no-repeat rule is scoped to a single run, not the whole board. A digit can appear many times on the grid as long as the copies sit in different across or down runs. This is what separates Kakuro from Sudoku-style thinking: you are not tracking "where has 7 gone," you are tracking "can 7 satisfy both the across sum and the down sum at this cell."

Why every cell is a two-constraint problem

Every white cell belongs to exactly one across run and one down run. A candidate digit is only useful if it works for both sums simultaneously. Before entering a number, check it against the across clue and the down clue at once — a digit that fits one but not the other is a dead end.

What a solved board looks like

A board is complete only when all four conditions hold:

1. Every white cell is filled.
2. Every across run equals its clue.
3. Every down run equals its clue.
4. No digit repeats within any single run.

If any one of these fails, the puzzle is not solved — even if the grid looks full.

Applying the rules on kakuro-puzzle.online

The site's guided first step shows the workflow: a yellow 3 clue on the left points to two white cells, which must sum to 3 without repeating, so you tap the first highlighted cell and press 1. From there:

• Select a white cell on the board, then enter a digit with the number pad.
• Use notes to pencil in candidates when a cell has several legal digits.
• Press Check only when ready — it reveals conflicts rather than solving for you.
• Use Hint, Undo, and Reset as recovery tools when a run goes wrong.

The board accepts standard Kakuro entries only; you never type sums or submit answers as text.

Common mistakes to avoid

• Treating a clue as a full row or column. Only the contiguous white run next to the clue counts.
• Allowing a repeated digit inside a run to make a sum work, such as 2+2 for a clue of 4.
• Ignoring the second constraint. Entering a digit that satisfies the across sum but breaks the down sum.
• Assuming a digit is "used up" board-wide. Repeats are legal across different runs.
• Checking too early. Check flags conflicts; it does not validate a partially built board as correct.

Once these three rules are automatic, most Kakuro progress comes from spotting sum combinations that have few legal digit sets — the puzzle is designed to be solved by logic rather than guessing.