How Kakuro Puzzles Work

In his book, "The Puzzle Instinct," author Marcel Danesi suggests that the human love of puzzles is both as mysterious and as innate as the laughter instinct. No one quite knows why people like to solve puzzles, just as no one knows why we laugh at something that amuses us. But Danesi does speculate that our love of puzzles can be chalked up to the same "mental catharsis" we love to feel at the resolution of dramatic suspense [source: Danesi]. Whatever the reason, it certainly feels good to solve a puzzle, evidenced by the crossword and sudoku puzzles that occupy honored places in the newspaper.

A kakuro puzzle is kind of a combination of the extremely popular crossword and sudoku puzzles. Like both crossword and sudoku, kakuro is easy to learn, but can range from simple to difficult to solve. An unsolved kakuro puzzle looks more like a crossword grid; the rules, however, are more similar to sudoku. Like sudoku, you solve kakuro by using logic to fill in the empty boxes with appropriate single digits (1 through 9). Unlike sudoku, however, kakuro also relies on math. Don't get intimidated just yet, though -- the only math required is simple addition.

In kakuro, each horizontal and vertical group of empty blocks comes with a "clue," which is a number. You solve the clue by filling in each group with numbers that add up to the clue number. The catch is that you can only use the numbers 1 through 9, and you can't repeat a number within one group. So, if the clue number is 4 and you have two boxes in the group, 2 and 2 won't work, because repeats aren't allowed in a group. Therefore, the only possible solutions are 1 and 3. But you still have to figure out exactly which box should be 1 and which should be 3. This will require finding out the possible solutions of other intersecting groups.

Kakuro also shares a similar history with sudoku. Although they have Japanese names, the Japanese are only credited with popularizing the games. The origins of kakuro are, in fact, American: The puzzle first appeared in 1950 in the United States. Dell Magazines published the game under the name "Cross Sums," and its inventor was a Canadian named James E. Funk [source: Shortz]. The game certainly has cross-cultural appeal, and it continues to challenge puzzle enthusiasts around the globe.

What's your best strategy for solving a kakuro puzzle? Add it all up on the next page.

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 on the next page.

Sources

• Danesi, Marcel. "The Puzzle Instinct: The Meaning of Puzzles in Human Life." Indiana University Press. 2002. (Aug. 31, 2011) http://books.google.com/books?id=B8UJgmZhdjMC
• 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) http://query.nytimes.com/gst/fullpage.html?res=9C03E6D61730F932A15750C0A9619C8B63
• Pluck, Kevin. "Kakuro Cross Sums Combinations Table." KevinPluck.net. 2005. (Aug. 31, 2011) http://www.kevinpluck.net/kakuro/KakuroCombinations.html
• Memmott, Carol. "In a Puzzling Development, Kakuro Beckons." USA Today. Dec. 8, 2005. (Aug. 31, 2011) www.usatoday.com/life/books/news/2005-12-07-kakuro_x.htm
• 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) http://www.nytimes.com/2007/03/21/business/21puzzle.html
• Stickels, Terry, Nathan Haselbauer. "The Big Book of Bathroom Bran-Sharpeners." Rockport Publishers. 2007. (Aug. 31, 2011) http://books.google.com/books?id=XHNpaZTvpscC
• Timmerman, Charles. "The Everything Kakuro Challenge Book." Everything Books, 2008. (Aug. 31, 2011) http://books.google.com/books?id=Loldfgoe6d8C