How to Play & Finish Kakuro Number Puzzles

If you’re looking for a new type of logic puzzle, Kakuro (also called “Cross Sums” or “number crosswords”) are perfect for testing your brain. These math-based puzzles can seem a little challenging at first, but there are tons of strategies to help you complete them. Keep reading, and we’ll cover the basic rules and number combinations, with wikiHow-exclusive advice from puzzle experts. We’ll even walk you through an example puzzle to help you understand the logic step-by-step!

Beginner Kakuro Solving Strategies

Puzzle experts Simon Anthony & Mark Goodliffe say that each clue tells you the sum of the numbers it’s pointing to. Answers can only contain the numbers 1–9, and the digits can’t be repeated. Here are a few tips for solving a puzzle:

Start with clues that are 2 blocks long to begin a puzzle easily.
Check for shared numbers where the clues intersect each other.
Write possible numbers lightly in pencil to keep track of solutions.
Isolate pairs of boxes that share the same possible numbers.
Take a break or work on a different part of the puzzle when you’re stuck.

Section 1 of 5:

How to Play Kakuro Puzzles

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Fill rows or columns with numbers 1-9 that sum up to the clue’s total. “Each clue gives a total for the sum of the number of cells that it is pointing to,” say Anthony & Goodliffe. They add that answers only use the numbers 1-9, and each digit can only be used once for each clue.^{[1]
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- Example: If the clue is 6 and has 2 empty squares, the possible numbers could be 1 + 5 or 2 + 4. The answer could not be 3 + 3 because the number repeats.
- Advanced example: “If the first clue in a puzzle says 29 and points to 4 cells, that would mean those 4 cells add up to 29,” say Anthony & Goodliffe. They add because you can’t repeat numbers, you might find that you have to use the numbers 9, 8, 7, and 5. Then, “you can use the clues going down to try to isolate which digit goes into which cell.”^{[2]
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- Clues for horizontal rows are listed in the top right triangle, and clues for vertical columns are listed in the bottom left triangle.
- A number can repeat in the same row or column as long as there’s at least 1 “clue” or shaded box between them.
Meet the wikiHow Expert

Simon Anthony & Mark Goodliffe are puzzle experts and the hosts of Cracking the Cryptic, a YouTube channel with nearly 700,000 subscribers where Simon and Mark solve puzzles live for the audience.

Section 2 of 5:

Strategies for Solving Kakuro Number Puzzles

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1
Start with 2-digit clues at first. Scan the puzzle for any clues that have an answer that’s 2 blocks long to use as starting points. Because there are fewer possibilities for which numbers fit, you can usually figure them out quickly and get some numbers on the grid early.
- Two-block clues that have a sum of 3, 4, 16, or 17 are the easiest to solve because they each only have 1 possible combination of numbers. Check out our section below for a full list of magic number combinations.
2
Check for intersections that share common numbers. When you’re looking at a clue, check the other clues that share boxes with it. List out the possible numbers that sum up to each clue, and check which ones have overlapping numbers. This can help you eliminate wrong answers and highlight the correct numbers.^{[3]
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- Example: If a 2-block row has a sum of 16 and a 2-block column has a sum of 17, the only possible values are 7-9 for the row and 8-9 for the column. That means the common value for the intersecting box is 9.
- Example: A 3-block row has the sum of 23 and intersects a 7-block column with a sum of 28. The horizontal row can only be 6 + 8 + 9. The vertical row can only be 1 + 2 + 3 + 4 + 5 + 6 + 7. The only digit in common is a 6, so that must be in the intersection.
3
Write possible numbers in the squares with a pencil. These small numbers, known as “pencil marks,” help you keep track of available options and prevent mistakes. Use a pencil to lightly write in the possible values for each clue in the blank boxes. As you keep working and figure out other clues, certain numbers will be eliminated from your pool of options, and you can erase those pencil marks.^{[4]
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- When you’re down to one digit left as a possible solution, you’ll know that’s the number you need to “officially” enter in the blank box.
4
Subtract a clue from 45 to get a hint about what’s missing. “The secret of Kakuro is that the digits 1–9 sum to 45,” say Anthony & Goodliffe. “So, if you see a six-cell clue in a Kakuro that adds to 38, you immediately know that the digits missing from that sequence must add to 7—so they must be 1, 2, and 4.”^{[5]
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- Anthony & Goodliffe continue, “You know that clue is only going to contain the digits 3, 5, 6, 7, 8, and 9.”^{[6]
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- They add that this type of logic is usually only needed for solving advanced Kakuro puzzles.^{[7]
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5
Look for boxes in the same clue that only have 2 options. When you’re writing potential numbers for each box, keep your eye out for any pairs that only have the exact same numbers. These squares have to contain either one of these numbers, so they are incorrect in any other box in that row or column.^{[8]
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- The same is true for any 3 squares that share the exact same 3 possible answers.
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Compare restrictions for crossing rows to make further deductions. If you already use a specific number in a row or column, it cannot be used again in that same row or column. That means you can eliminate it as an option from any other box from the crossing clues.^{[9]
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- Example: A 4-block row with a sum of 27 crosses shares a 3 with a completed column. Check the intersections of other boxes in the row and remove 3 as a potential option from any of those squares.
7
Look for boxes that only have 1 option left. Since numbers can only be used once in a row or column, figuring out the last remaining blank box comes pretty easily once you fill in the others. Double-check for any single boxes you missed and fill them in with the missing digit.
- Example: If a clue has the sum of 6 and you placed a 5 in one of the squares already, you can confidently place a 1 in the empty square.
If you’re really stuck and can’t deduce numbers for one part of the puzzle, look for another clue that has an easy starting point. Sometimes, finishing a different part of the puzzle creates more restrictions on the original clue you were trying to solve.

Section 3 of 5:

Kakuro Magic Number Combinations

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Memorize the combinations for specific numbers and block sizes. Some clues only have one possible combination of numbers, depending on the number of blocks in the solution. Learning these combinations can help you quickly analyze your puzzle and fill in the potential options.^{[10]
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- 2 blocks
  - 3: 1 + 2
  - 4: 1 + 3
  - 16: 7 + 9
  - 17: 8 + 9
- 3 blocks
  - 6: 1 + 2 + 3
  - 7: 1 + 2 + 4
  - 23: 6 + 8 + 9
  - 24: 7 + 8 + 9
- 4 blocks
  - 10: 1 + 2 + 3 + 4
  - 11: 1 + 2 + 3 + 5
  - 29: 5 + 7 + 8 + 9
  - 30: 6 + 7 + 8 + 9
- 5 blocks
  - 15: 1 + 2 + 3 + 4 + 5
  - 16: 1 + 2 + 3 + 4 + 6
  - 34: 4 + 6 + 7 + 8 + 9
  - 35: 5 + 6 + 7 + 8 + 9
- 6 blocks
  - 21: 1 + 2 + 3 + 4 + 5 + 6
  - 22: 1 + 2 + 3 + 4 + 5 + 7
  - 38: 3 + 5 + 6 + 7 + 8 + 9
  - 39: 4 + 5 + 6 + 7 + 8 + 9
- 7 blocks
  - 28: 1 + 2 + 3 + 4 + 5 + 6 + 7
  - 29: 1 + 2 + 3 + 4 + 5 + 6 + 8
  - 41: 2 + 4 + 5 + 6 + 7 + 8 + 9
  - 42: 3 + 4 + 5 + 6 + 7 + 8 + 9
- 8 blocks
  - 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
- 9 blocks
  - 45: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9

Section 4 of 5:

Step-by-Step Kakuro Logic Example

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In the example puzzle, the 16 clue only takes up 2 blocks. The only possible numbers that add up to 16 in a puzzle are 7 and 9, so write them both as possibilities in the boxes.
2
Cross-reference the 10 clue to place the row numbers. The vertical 10 clue takes up 3 blocks, so you can deduce that none of them can contain a 9. Since the 9 can’t be in the same column as the 10, you can confirm the 7 and 9 squares for the 16 clue.
- The remaining squares in the 10 column have to be either 1 or 2, but you don’t know which order yet. Write both numbers in each square.
The top row of 2 squares has a total sum of 11. Only the digits 1 through 9 are used in the puzzle, so you can’t place 1 and 10 in that row. This confirms the 2 in the square it shares with the 10 clue and the 1 in the remaining square.
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Fill in the remaining squares to complete the puzzle. The remaining empty spots are all part of 2-square answers, so just subtract the filled-in number from the sum in the clue. This confirms a 9 in the remaining square for the horizontal 11 clue and a 4 for the horizontal 5 clue.
- Double-check the clue in the column to confirm your answers. 9 + 4 equals 13, so you have all the numbers placed correctly!

Section 5 of 5:

Similar Games to Kakuro Puzzles

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Try these other games when you’re finished working on kakuro puzzles. There are tons of other games and puzzles that test your logic, and they all have slightly different rules and goals. Check out our guides on these other puzzle types to keep your mind sharp:
- Sudoku: Fill in each row, column, and square with the digits 1-9 so they never intersect.
- Kenken: Fill boxes with numbers inside “cages” with specific equations.
- Crossword puzzles: Solve the clues to fill the grid with interlocking words and letters.
  - Anthony & Goodliffe say that Kakuro is like a cross between Sudoku and a crossword puzzle—so if you like Kakuro, you’ll probably love those puzzles, too!^{[11]
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Did you know? Anthony & Goodliffe say that Jason Zuffranieri currently holds the title as the world’s fastest Kakuro player. They say his speed is “very hard to comprehend, even if you are supremely gifted at arithmetic."^{[12]
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Expert Interview} Zuffranieri is also a Jeopardy Hall of Famer!

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