Print the PDF and slip it inside a puzzle book, or keep the page open beside our kakuro puzzles. The notes below cover reading the table, the entries to memorize, and the habit that turns the sheet from a reference into a solving tool: crossing two runs at once.
Reading the table by run length
Find the run length first, then the clue. Each entry is a set of digits that may sit in any order along the run. A two-cell run of 4 shows only 1 3, because the other way to make 4, 2+2, repeats a digit and is never allowed.
Each run length has a fixed range. Two cells cover 3 to 17, three cells 6 to 24, four cells 10 to 30, and so on up to nine cells, which can only ever make 45. A clue near either end of its range has very few sets, and the highlighted ones have exactly one.
Runs that fill themselves
These are the one-way runs. Learn the two- and three-cell ones first, since short runs turn up all over every board.
- 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
- 5 cells: 15, 16, 34 and 35; 6 cells: 21, 22, 38 and 39; 7 cells: 28, 29, 41 and 42
- 8 cells: every clue is one way, because a single digit is missing and it equals 45 minus the clue
- 9 cells: always 1 to 9, total 45
Cross two runs, not one
A white cell belongs to an across run and a down run, and it can only hold a digit both runs allow. This is the move the sheet is really for. Say a cell sits in an across run of 3 in two cells and a down run of 4 in two cells. The first allows 1 and 2, the second 1 and 3, so the cell is 1, the rest of the across run is 2 and the rest of the down run is 3.
The same trick works at the high end. A cell shared by a two-cell 16 (7 and 9) and a three-cell 23 (6, 8 and 9) can only be 9. Place it and the other cell of the 16 is 7, while the rest of the 23 must be 6 and 8 in some order.
Reading the multi-option clues
A clue with two or three sets can still pin down a digit. A three-cell 8 is 1+2+5 or 1+3+4, so the run holds a 1. A four-cell 12 is 1+2+3+6 or 1+2+4+5, so it holds both 1 and 2. A four-cell 28 is 4+7+8+9 or 5+6+8+9, so it holds 8 and 9. When only one cell of the run can take that certain digit, the digit goes there.
Long runs are easier to think about through what they leave out. A seven-cell run of 30 uses every digit except two that add up to 15, so the missing pair is 6 and 9 or 7 and 8. An eight-cell run of 40 is missing only the 5.
Using the sheet as you solve
Every time you place a digit, the run it sits in becomes a shorter run with a smaller clue. Three cells summing to 19 with a 9 already placed leave two cells needing 10 without a 9, so 1+9 drops out and the pair is 2+8, 3+7 or 4+6. Look up the shrunken run instead of the original one and the candidates fall faster.
Kakuro shares this arithmetic with killer sudoku cages, so the killer sudoku cheat sheet is the same table arranged for cages. For the full set of techniques, from first runs to whole-run analysis, see how to solve kakuro, and for the rules themselves, kakuro rules.