As we have seen, in Kakuro puzzles there are some clues with only one solution (like the 3 can only be made by 1 and 2), and others with a large number of possibilities. The tables below list the possibilities for all lengths of clues, with the bold entries showing the unique solutions for that clue.
As well as being useful for solving Kakuro puzzles, exactly the same principles also apply to Killer Sudoku puzzles too, so the same combinations can also be used there.
| Two | Three | Four | |
|---|---|---|---|
| 3 | 1.2 | ||
| 4 | 1.3 | ||
| 5 | 1 to 4 | ||
| 6 | 1,2,4,5 | 1.2.3 | |
| 7 | 1 to 6 | 1.2.4 | |
| 8 | 1 to 7 | 1 to 5 | |
| 9 | 1 to 8 | 1 to 6 | |
| 10 | any | 1 to 7 | 1.2.3.4 |
| 11 | 2 to 9 | 1 to 8 | 1.2.3.5 |
| 12 | 3 to 9 | any | 1 to 6 |
| 13 | 4 to 9 | any | 1 to 7 |
| 14 | 5,6,8,9 | any | 1 to 8 |
| 15 | 6,7,8,9 | any | any |
| 16 | 7.9 | any | any |
| 17 | 8.9 | any | any |
| 18 | any | any | |
| 19 | 2 to 9 | any | |
| 20 | 3 to 9 | any | |
| 21 | 4 to 9 | any | |
| 22 | 5 to 9 | any | |
| 23 | 6.8.9 | any | |
| 24 | 7.8.9 | any | |
| 25 | any | ||
| 26 | 2 to 9 | ||
| 27 | 3 to 9 | ||
| 28 | 4 to 9 | ||
| 29 | 5.7.8.9 | ||
| 30 | 6.7.8.9 |
| Five | Six | Seven | |
|---|---|---|---|
| 15 | 1.2.3.4.5 | ||
| 16 | 1.2.3.4.6 | ||
| 17 | 1 to 7 | ||
| 18 | 1 to 8 | ||
| 19 | any | ||
| 20 | any | ||
| 21 | any | 1.2.3.4.5.6 | |
| 22 | any | 1.2.3.4.5.7 | |
| 23 | any | 1 to 8 | |
| 24 | any | any | |
| 25 | any | any | |
| 26 | any | any | |
| 27 | any | any | |
| 28 | any | any | 1.2.3.4.5.6.7 |
| 29 | any | any | 1.2.3.4.5.6.8 |
| 30 | any | any | any |
| 31 | any | any | any |
| 32 | 2 to 9 | any | any |
| 33 | 3 to 9 | any | any |
| 34 | 4.6.7.8.9 | any | any |
| 35 | 5.6.7.8.9 | any | any |
| 36 | any | any | |
| 37 | 2 to 9 | any | |
| 38 | 3.5.6.7.8.9 | any | |
| 39 | 4.5.6.7.8.9 | any | |
| 40 | any | ||
| 41 | 2.4.5.6.7.8.9 | ||
| 42 | 3.4.5.6.7.8.9 |
| Eight | Nine | |
|---|---|---|
| 36 | 1.2.3.4.5.6.7.8 | |
| 37 | 1.2.3.4.5.6.7.9 | |
| 38 | 1.2.3.4.5.6.8.9 | |
| 39 | 1.2.3.4.5.7.8.9 | |
| 40 | 1.2.3.4.6.7.8.9 | |
| 41 | 1.2.3.5.6.7.8.9 | |
| 42 | 1.2.4.5.6.7.8.9 | |
| 43 | 1.3.4.5.6.7.8.9 | |
| 44 | 2.3.4.5.6.7.8.9 | |
| 45 | 1.2.3.4.5.6.7.8.9 |
For example, the clue 7 in three squares is given as 1.2.4 which means that's the only solution (the "no repeats" rule forbids others like 2.2.3 and 1.3.3). The clue 12 in four squares is given as "1 to 6", which means it definitely contains a 1 but no numbers above 6, whereas clue 18 in four squares is just given as "any" - more clues are needed!
On the internet you can find more comprehensive tables showing every possible combination up to 9 squares long, but often this shortened version of the cheat sheet is more useful and easier to work with.