A New Name for an Old Friend

Kakuro is the Japanese name for the type of puzzle known in the U.S. as cross sums. I have been solving this type of logic puzzle for the past couple of decades. Kakuro and Sudoku are the two most widely available Japanese logic puzzles in the U.S. While Sudoku is purely a logic puzzle which does not require any math to solve, Kakuro requires both logic and simple arithmetic to be successfully solved.

Kakuro can be thought of as a numeric version of the classic crossword puzzle. Each row and column (i.e. words in a classic crossword puzzle) add up to the number at the top or left. In addition, the puzzle only uses the numbers 1 through 9 and they are not duplicated within any "word". Here is a simple example of a Kakuro or cross sum puzzle.

In this particular puzzle, the digits in the first "word" across (in the upper left hand corner), add up to the value 12. The digits in the first "word" down (also in the upper left hand corner), add up to the value 6. Since no digits are repeated within any "word", we know that the only three unique digits to add up to 6 are: 1, 2, and 3. We also know that since the largest possible digit is 9, the upper left hand box must contain the number 3. This means that the box immediately to its right must contain the digit 9 (12 - 3 = 9). Similarly, we know that the three digits summing to 23 are: 9, 8, and 6. We already know where the 9 goes. The box below the 9 can only contain the number 6 since 8 > 7. This allows us to place the digits 6 and 8 in the two boxes below the 9. In turn that allows us to place a 1 and 2 below the 3. Continuing in this fashion, it is possible to find a unique solution for the entire puzzle which is shown below:

In a future post, I will share some useful tips for solving Kakuro puzzles. So stay tuned for more information!

Welcome

About a year ago I received a totally unexpected gift, a Japanese book of logic puzzles.  In addition to the wildly popular Sudoku puzzles, the book had ten other kinds of logic puzzles.  Some of these puzzles involved numbers like Sudoku while others were strictly graphical in nature.  They all had their own set of simple rules.  There were about 250 puzzles covering a wide range of complexities.

The book and its puzzles were an instant hit for me.  I have spent many happy hours working on the various puzzles.  A year has gone by and I am about 75% finished with the book.  Since then, I have ordered two more books from the same company.  In addition to simply solving these puzzles, I am interested in exploring the theory behind creating and solving these puzzles.  I have decided to create this blog as a way to share my exploration of these puzzles.  Hopefully, it will also provide a method for some collaboration along the way.

In the weeks and months to come, you can expect to see a wide variety of posts ranging from descriptions of the various puzzles and their rules to tips and tricks I have discovered for attacking and solving them.  Eventually, I would like to see this expand into discoveries of methods for automatic puzzle creation and solving.

Hopefully, this blog will also help spread the word about a whole genre of puzzles which are similar to Sudoku but provide exciting variety.