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Kakuro - Free Online Cross-Sum Puzzle

Fill each run with 1–9 so it adds up to the clue

Puzzle
Time
0:00
Mistakes
0
Best

Fill the runs to hit each sum

Each clue is the total of the run beside it. Use digits 1–9 with no repeats inside a run. Pick a puzzle to begin.

About the Kakuro

Kakuro is like a crossword built from sums instead of words. The grid is split into horizontal and vertical runs of white cells, and every run carries a clue — the total its digits must add up to. You fill each run with the numbers 1 to 9 so it hits that sum exactly, and no digit may repeat within a single run. That one rule, combined across intersecting runs, is enough to pin down every cell by pure logic. It has been called a mathematical cousin of Sudoku, and once the deductions click it is every bit as moreish. Fresh puzzles are generated each time across two sizes.

How to play

  1. Pick a puzzle. Each clue is the sum of the run beside or below it.
  2. Tap a white cell, then tap a number 1–9 (or type it) to place it.
  3. A run must total its clue with no digit repeated inside it.
  4. Fill every cell so all runs balance — that wins the puzzle.

What it measures

This test focuses on your logical reasoning, arithmetic fluency and working memory. A Mini Kakuro falls in a few minutes once you spot the tight runs; a Classic grid rewards patient, systematic deduction. A clean, no-mistake solve is the real benchmark.

Why play it

  • Combines logic with light mental arithmetic — a dual workout
  • The no-repeat-in-a-run rule trains the same elimination logic as Sudoku
  • Cross-referencing intersecting sums is a genuine working-memory exercise

Did you know?

  • Kakuro began as "Cross Sums" in American puzzle magazines before Japan's Nikoli renamed and popularised it in 1980.
  • The name is a Japanese contraction of "kasan kurosu" — literally "addition cross".
  • Certain sums force their digits: a run of two cells totalling 3 can only be 1 and 2, which is where solvers start.
  • Before Sudoku's global boom, Kakuro was the best-selling logic puzzle in Japan.

What counts as a good score?

No published norms exist for this format, so the ranges below are practical skill tiers rather than measured population data.

Level Puzzle size handled What it means
Learning Small grids, obvious sums Relying on the forced combinations — sums with exactly one possible digit set.
Comfortable Medium grids Recognising common combinations without deriving them each time.
Strong Large grids Cross-referencing row and column combinations to eliminate candidates efficiently.
Expert Grids with few forced entries Comfortable when nothing is immediately determined and progress needs chained elimination.

Tiers describe grid complexity rather than measured solve times. Kakuro difficulty depends mostly on how many entries have multiple valid combinations.

How to improve your kakuro score

1.Memorise the forced sums

Some sums have exactly one digit set: 3 in two cells is 1+2, 4 is 1+3, 16 in two cells is 7+9, 45 in nine cells uses every digit. These are free entries.

2.Work the intersections

A cell sits in both a row and a column sum. Intersect the two candidate sets — the answer is usually far more constrained than either alone.

3.Remember digits never repeat

No digit appears twice within a single sum. This eliminates far more candidates than beginners expect.

4.Start with the shortest entries

Two-cell sums have the fewest combinations and therefore the tightest constraints. Build outward from them.

5.Use extremes

Very low and very high sums for a given length are the most constrained. A 6 in three cells can only be 1+2+3.

A crossword that predates Sudoku

Kakuro appeared as "Cross Sums" in Dell Pencil Puzzles and Word Games in 1966, credited to Canadian designer Jacob E. Funk. Nikoli imported it to Japan in 1980 under the name Kasan Kurosu — addition cross — which contracted to Kakuro. Before Sudoku's global breakout in 2004, Kakuro was the more popular of the two in Japan.

Unlike Sudoku, Kakuro genuinely requires arithmetic, but the arithmetic is shallow: the real work is combinatorial, narrowing which digit sets can produce a sum in a given number of cells. Experienced solvers work almost entirely from memorised combination tables.

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Frequently Asked

How do you play Kakuro?

Each clue gives the total for the run of white cells to its right (for a number in the top-right of a black cell) or below it (bottom-left). Fill those cells with digits 1–9 so they add up to the clue, never repeating a digit within the same run. Intersecting runs constrain each other until every cell is forced.

Can a digit repeat in Kakuro?

Not within a single run. A horizontal or vertical run must use distinct digits from 1 to 9. The same digit can appear elsewhere in the grid, just not twice in the same run — which is the key to solving by elimination.

Is Kakuro just maths?

There is light addition, but Kakuro is really a logic puzzle. The arithmetic only narrows the possibilities; deduction — combining what each intersecting run allows — is what actually solves it, exactly like Sudoku.

Do I need to be good at maths?

No. The sums involved are small additions, and most experienced solvers work from memorised combination sets rather than calculating. The skill is combinatorial elimination, not arithmetic.

Can a digit repeat in the same sum?

Never. Each digit 1–9 appears at most once in any single run, and that constraint does most of the work in narrowing candidates.

References

  1. Nikoli — Kakuro puzzle history.