The rules, in one minute
A kakuro grid is a crossword made of numbers. Instead of word clues, each shaded cell carries one or two small totals:
- A number in the top right of a clue cell is the total of the white run stretching across, to its right.
- A number in the bottom left is the total of the run heading down, below it.
- Fill every white cell with a digit from 1 to 9. Each run must add up to its clue, and no digit may repeat within a run. A digit may repeat elsewhere in the grid, just never inside the same run.
That no-repeat rule is what makes kakuro a logic puzzle rather than an arithmetic quiz. A two-cell run summing to 4 cannot be 2 and 2. It must be 1 and 3, and knowing that is a solving tool.
A promise worth knowing: a properly set kakuro has exactly one solution and can be finished by deduction alone. If you ever feel forced to guess, there is a deduction you have not spotted yet, and that is good news: it means the next move is findable.
Your first solve, step by step
Here is a small puzzle with two across runs and two down runs. The 4 and 6 clue the two columns; the 3 and 7 clue the two rows.
The starting grid: columns must sum to 4 and 6, rows to 3 and 7.
Step 1: find the tightest clue
The across 3 is as tight as a clue gets. Two different digits that sum to 3 can only be 1 and 2. We do not yet know which cell holds which, so pencil both digits into both cells as candidates.
Step 2: cross it with another run
The down 4 is nearly as tight: two different digits summing to 4 can only be 1 and 3 (2 and 2 would repeat). Now look at the cell where these two runs cross, the top-left white cell. Across says it is 1 or 2. Down says it is 1 or 3. Only 1 satisfies both, so that cell is settled. No guessing happened; the two clues simply left one digit standing.
The crossing of 3-across and 4-down can only hold a 1, and placing it strikes the 1 from the pencilmarks beside and below it.
Step 3: let the answer ripple
Every placed digit tightens its runs. The across 3 already has its 1, so its other cell must be 2. The down 4 already has its 1, so the cell below it must be 3.
Step 4: check the finish
One cell remains, and both of its clues agree on it. The across 7 has a 3 so far, so it needs a 4. The down 6 has a 2 so far, so it also needs a 4. When both runs ask for the same digit, the grid is telling you it is done.
Solved: 1 + 2 = 3 across, 3 + 4 = 7 across, 1 + 3 = 4 down, 2 + 4 = 6 down.
The habit that carries you
Everything you just did scales up. Real puzzles are bigger, but the loop is the same: find the tightest clues, pencil in their few possibilities, and look at the crossings, because a cell must satisfy both of its runs at once. When you are ready for the patterns that make bigger grids fall, the techniques guide is next, and the combinations chart lists every clue's possibilities so you never have to work them out by hand.
Learn by solving
Kakuro Haven starts with a 25-level teaching ramp that grows from a tiny grid like the one above into full puzzles at a comfortable pace. All 2,000+ puzzles are free, and there is never an ad while you solve.
