Free printable kakuro puzzles and tools

Kakuro Cheat Sheet and Combinations Calculator

Choose the number of cells and the sum to see every digit combination, or print the full kakuro combination chart.

A kakuro cheat sheet is a list of every set of digits that adds up to a given sum, so you can check which numbers fit a run before you write anything in. This page offers one as a free kakuro combinations calculator and a full kakuro combination chart. It runs in your web browser with no sign-up, and nothing you enter is uploaded or sent to a server. Use the calculator when you have a specific run in mind, such as 3 cells adding to 7. Use the chart to see every sum for 2 to 9 cells at once. The chart is set up as an easy printable kakuro cheat sheet on Letter or A4 paper, and the same digit sets apply to killer sudoku cages.

How to use the kakuro combinations calculator

  1. Set Number of cells to the length of your run, from 2 to 9.
  2. Type the clue into Sum. The hint under the box shows the possible range for your cell count, such as “3 cells: sums from 6 to 24”. With 9 cells, the only possible sum is 45.
  3. Read the results. You will see the number of combinations, each written like 1 + 9, the digits that appear in every combination, and the digits that never appear.
  4. If you know a digit is in the run, press it under Must include. If you know it is not, press it under Must exclude. A digit can’t sit in both rows, because picking it in one row removes it from the other.
  5. Check the note. If the sum has exactly one combination, or your include and exclude choices leave only one, the tool tells you which one. For example, 3 cells adding to 7 can only be 1 + 2 + 4.
  6. Press Reset to return to 3 cells and sum 15.

The settings are stored in the page address, such as ?cells=3&sum=7. Press Copy link to share a specific setup. Below the calculator, the chart lists every sum in a table for each size. Unique rows are highlighted and marked “unique”. Use the Show select to view one size, tick Unique combinations only to narrow the list, or click any sum to load it into the calculator.

To print, pick Letter or A4 under Paper, then press Print cheat sheet.

What are the unique kakuro combinations?

A unique kakuro combination is a sum that can be made from only one set of different digits for a given number of cells. The tool finds 34 such sums across 2 to 9 cells. For 2 cells they are 3 (1+2), 4 (1+3), 16 (7+9) and 17 (8+9). For 3 cells they are 6 (1+2+3), 7 (1+2+4), 23 (6+8+9) and 24 (7+8+9). For 4 cells they are 10, 11, 29 and 30. For 5 cells they are 15, 16, 34 and 35. For 6 cells they are 21, 22, 38 and 39. For 7 cells they are 28, 29, 41 and 42. For 8 cells every sum from 36 to 44 is unique, because each one leaves out a single digit. For 9 cells the sum is always 45.

Unique sums are the best place to start solving. If a run has a unique sum, its digits are known for certain. You can then check the across and down runs that share a cell with it, and keep only the digits that both runs still allow.

How many combinations are there for a kakuro sum?

A kakuro run uses different digits from 1 to 9 that add up to the clue, and no digit can repeat inside a run. A combination is one set of such digits with the right total, written in any order. The sums that can be reached depend on the number of cells, n. The smallest possible total is n(n+1)/2, and the largest is n(19-n)/2. So 2 cells can make sums from 3 to 17, 3 cells from 6 to 24, and 4 cells from 10 to 30. A sum outside that range has no combinations at all.

Across 2 to 9 cells there are 120 cell-and-sum pairs and 502 combinations in total. The sum with the most combinations is 4 cells adding to 20, which has 12. Counts for a single sum can be small. For 2 cells adding to 10 there are four combinations, 1+9, 2+8, 3+7 and 4+6, so the digit 5 never appears. For 2 cells adding to 15 there are two, 6+9 and 7+8.

There is also a shortcut. The digits left out of a set always add up to a fixed total. A set of k digits adding to s leaves 9 − k digits adding to 45 − s. So an 8-cell run adding to s leaves out only the single digit 45 − s, and the 7-cell chart mirrors the 2-cell chart.

Frequently asked questions

Can I print the kakuro cheat sheet or save it as a PDF?

Yes. Choose Letter or A4 under Paper, then press Print cheat sheet. The full chart prints on two pages, black on white, with unique rows boxed. To get a PDF, choose Save as PDF in the print window. If you tick Unique combinations only first, it prints as one page with the 34 unique sums.

Does the cheat sheet work for killer sudoku?

Yes. Cages in killer sudoku also cannot repeat a digit, so the same combinations apply to a cage of 2 to 9 cells. Check the cage size and total, then use the calculator or chart to see which digit sets are possible.

What does “must include” do?

It limits the results to combinations that contain the digit you press. For example, 3 cells adding to 15 with 1 under Must include and 9 under Must exclude leaves only 1 + 6 + 8. Digits chosen under Must exclude are removed from every result.

Why can a 2-cell run never add up to 2 or 18?

Both cells in a run must hold different digits. The smallest possible total is 1 + 2 = 3, and the largest is 8 + 9 = 17. A total of 2 would need 1 + 1, and a total of 18 would need 9 + 9, and both repeat a digit. That is why 2-cell sums run from 3 to 17.

Is the kakuro combination chart free to use?

Yes. The tool is free, runs in your browser, and needs no sign-up. Nothing you enter is uploaded or sent to a server.