How to Play Kakuro
New to Kakuro — sometimes called Cross Sums? Think of it as a numeric crossword: fill the white cells with digits 1–9 so that each across or down run adds up to its clue, with no digit repeating inside a run. It uses addition, but at heart it is a logic puzzle. This guide covers the rules and your first moves.
How to play Kakuro, step by step
- Get to know the grid — Kakuro mixes black clue cells with white answer cells; a clue cell shows a sum for the run of white cells to its right (across) or below it (down).
- Learn the rules — fill each run with digits 1 to 9 that add up to the run’s clue, and never repeat a digit within the same run.
- Start with short runs — a two-cell run summing to 3 can only be 1+2, and one summing to 17 can only be 8+9; these forced pairs place digits instantly.
- Use the unique sums — many clues have only one set of digits, such as 6 in three cells = 1+2+3, which narrows a whole run at once.
- Cross-check across and down — every white cell sits in one across run and one down run, so its digit must fit both sums.
- Eliminate by overlap — where an across combination and a down combination meet, only a digit common to both can go in that shared cell.
- Never guess — a proper Kakuro has one logical solution; keep deducing from the sum combinations until every cell is filled.
What is Kakuro?
Kakuro is a logic puzzle that looks like a crossword filled with numbers: you place digits 1–9 in the white cells so that each run of cells adds up to the clue at its start, without repeating a digit inside that run. It is also published as Cross Sums.
Although you add the digits, success comes from logic, not arithmetic skill — the real game is working out which digits can make a sum given the no-repeat rule and the crossing runs.
Reading the clues
Each clue number sits in a black cell and applies to the run of white cells it points into — a number in the upper-right triangle is the total for the run going across, and one in the lower-left triangle is the total for the run going down.
So a black cell can carry two clues at once: one for the cells to its right and one for the cells below. Every white cell therefore belongs to exactly one across run and one down run, and its digit has to satisfy both totals.
Magic combinations: your fastest moves
The quickest way into a Kakuro is the "magic" combinations — sums that can be made in only one way, so they place a whole run’s digits with no guesswork.
- Two cells summing to 3 → {1, 2}; to 4 → {1, 3}; to 16 → {7, 9}; to 17 → {8, 9}.
- Three cells summing to 6 → {1, 2, 3}; to 24 → {7, 8, 9}.
- The lowest and highest totals for any run length always have a single combination.
Place these first, then use the crossing runs to decide the order of the digits within each combination.
Kakuro for beginners: FAQ
Is Kakuro a maths puzzle?
Kakuro uses addition, but it is really a logic puzzle. You succeed by working out which sets of digits can make each sum under the no-repeat rule and how the crossing runs constrain each other — not by being fast at mental arithmetic.
What are the rules of Kakuro?
Fill the white cells with digits 1 to 9 so that each horizontal and vertical run adds up to the clue shown in the black cell at its start, and no digit repeats within the same run. Each white cell belongs to one across run and one down run, and must satisfy both.
What is a magic combination in Kakuro?
A magic combination is a sum that can be formed in only one way for a given run length — for example, two cells summing to 17 must be 8 and 9, and three cells summing to 6 must be 1, 2 and 3. They let you fill a run’s digits with certainty and are the best place to start.
Can a digit repeat in Kakuro?
Not within a single run. A digit can appear elsewhere in the grid, but never twice in the same across or down run. That no-repeat rule is what makes the sum clues solvable by logic.
Can every Kakuro be solved without guessing?
Yes — a properly made Kakuro has exactly one solution reachable by logic alone. Every board here is generated and checked to guarantee that single, logical solution, so you never need to guess.