How to Play Kakuro

➕What is Kakuro?

Kakuro is the arithmetic cousin of the crossword: a grid of black and white cells where your answers are digits and your "clues" are sums. Each black cell may carry a clue for the run to its right (across) and a clue for the run below it (down). Fill each white cell with a digit 1–9 so every run adds up to its clue — with no digit repeated inside a single run. Like Sudoku, every DailyGrid Kakuro has exactly one solution.

📜The rules

1. White cells take digits 1–9. (Zero never appears in Kakuro.)
2. Each run — a straight block of white cells — must sum exactly to its clue.
3. No digit may repeat within a single run. The same digit can appear twice in a row or column if the cells are in different runs, separated by a black cell.
4. A run's length is set by the grid: a clue of 16 over 2 cells is a very different problem from 16 over 5 cells.
5. Fill every white cell to solve.

🎯Strategy

Getting started — memorize the magic sums

• Some sum/length pairs have only one possible combination. These are gifts — write their digits as candidates immediately:
  2 cells: 3 = 1+2 · 4 = 1+3 · 16 = 7+9 · 17 = 8+9
  3 cells: 6 = 1+2+3 · 7 = 1+2+4 · 23 = 6+8+9 · 24 = 7+8+9
  4 cells: 10 = 1+2+3+4 · 11 = 1+2+3+5 · 29 = 5+7+8+9 · 30 = 6+7+8+9
• Start where two short runs cross. A cell at the intersection of a 2-cell across and a 2-cell down has very few options — often one.
• Extreme sums restrict hardest. Very low and very high clues have few combinations; middling sums (like 20 in 5 cells) have many. Work the extremes first.

Level up

• Intersect the combination lists. For each cell, its across run allows one set of digits and its down run another — the cell must be in both sets.
• Run arithmetic: if a run of 3 must sum to 20 and two cells are forced to 9 and 8, the third is 3 — check forced remainders after every placement.
• The 45 rule: a full row or column of nine white cells always sums to 45. Where a long run overlaps others, subtracting known sums from 45 exposes the hidden cell.
• Pencil candidates in every cell and prune by run membership — Kakuro is Sudoku's candidate game with sums on top.

Pro tips

• Learn pairs by complement: for 2-cell sums, each digit's partner is fixed (for 12: 3+9, 4+8, 5+7). Seeing a 3 in a 12-run instantly places the 9.
• Try the ✏️ No Pencil variation only after the combination table is muscle memory — it's the true Kakuro hard mode.

⚠️Common mistakes

• Repeating a digit inside one run because the cells aren't adjacent — the rule covers the whole run, not just neighbors.
• Forgetting the length: 16 in 2 cells forces 7+9, but 16 in 4 cells has several options. Always read sum and length together.
• Treating runs like Sudoku houses — a digit may legally repeat in a line across a black-cell break.

❓FAQ

What are the rules of Kakuro?

Fill white cells with digits 1–9 so each run sums to its clue, with no digit repeated inside a single run. Digits may repeat across a black-cell break.

Which sums should I memorize?

The unique ones: 3, 4, 16, 17 in two cells; 6, 7, 23, 24 in three; 10, 11, 29, 30 in four. They're listed in the strategy section.

Is the DailyGrid Kakuro free?

Yes — a new Kakuro every day at midnight ET, no account needed — the daily puzzles are free. Always. One of ten daily puzzles on DailyGrid.

Where can I learn the other games?

See all ten DailyGrid guides.