How Kakuro Puzzles Work

How do you solve kakuro puzzles?

Through practice, people come up with their own favorite strategies for solving kakuro puzzles, but it really all comes down to logic. If you don't consider it cheating, many online resources for the game and books of kakuro puzzles contain a list of all the possible solution combinations. In other words, a full table will include all of the possible solution sets for each possible clue number for each possible number of boxes. So, if you have to solve a clue of 8 in two boxes (described as "8 in two"), the table will list three possible solution sets: 1 and 7, 2 and 6, or 3 and 5.

This table can serve as a nice "cheat sheet," especially for beginners. But more advanced players should take no shame in sneaking a peak at it once in a while. Suppose your clue is 25 with five boxes ("25 in five"). There are 12 unique solution sets that could possibly solve that clue -- and, on top of that, you still need to figure out which digits go in which box.

Once you've determined all of the possible solution sets for a given clue, you can compare them to the possible solution sets for an intersecting group. By "intersecting group," we mean one that shares a box with another. So, a horizontal group of four boxes can share common boxes with four vertical groups -- each with its own clues and possible solution sets. You can rely on process of elimination to narrow down and solve which digits go where. The simplest example of this is if a "4 in 2" intersects with a "3 in 2." Each group must contain a 1, so the intersecting box must be 1.

Although it all comes down to logic, some effective tips will help you on your way to becoming a master kakuro puzzler. For instance, to help you remember, use a pencil to make small notes of the possible solutions in each box. Erase or cross out the numbers as the process of elimination dictates. It also makes sense to start with the easiest clues, in the hopes that those solutions will unlock harder ones. So, look for groups with the fewest boxes, and look for clues that are either small numbers or large numbers. These will tend to have the fewest number of solution sets.

Most of all, of course, the best teacher is practice. For lots more information on kakuro and puzzles, tally the links below.

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  • Danesi, Marcel. "The Puzzle Instinct: The Meaning of Puzzles in Human Life." Indiana University Press. 2002. (Aug. 31, 2011)
  • Fackler, Martin. "After Sudoku, What's Next?; Hint: Japan's Master of Popular Puzzles May Already Know." The New York Times. March 21, 2007. (Aug. 31, 2011)
  • Pluck, Kevin. "Kakuro Cross Sums Combinations Table." 2005. (Aug. 31, 2011)
  • Memmott, Carol. "In a Puzzling Development, Kakuro Beckons." USA Today. Dec. 8, 2005. (Aug. 31, 2011)
  • Shortz, Will. "A Rush of Excitement, From Filling Empty Spaces to Completing a Large Loop." The New York Times. March 21, 2007. (Aug. 31, 2011)
  • Stickels, Terry, Nathan Haselbauer. "The Big Book of Bathroom Bran-Sharpeners." Rockport Publishers. 2007. (Aug. 31, 2011)
  • Timmerman, Charles. "The Everything Kakuro Challenge Book." Everything Books, 2008. (Aug. 31, 2011)