Fig. 1: Sample unsolved Kakuro puzzle

We’ve now arrived at my favorite Japanese logic puzzle, Kakuro.  Like Sudoku, Kakuro is not Japanese in origin.  Dell Puzzles in America is credited with the first Kakuro puzzles in the 1960’s, which they called Cross Sums.  While Cross Sums were somewhat popular in America, they didn’t truly catch on until the Japanese puzzle company Nikoli rebranded Cross Sums as Kakuro in the 1980’s and its popularity exploded in Japan.  Today Kakuro’s popularity in Japan is second only to Sudoku, and while it is not as popular in America, it is one of the more well-known Japanese logic puzzles.

The rules of Kakuro combine Sudoku with arithmetic.  Black boxes, much as in crosswords, separate rows and columns into smaller subrows, or sub columns.  Like Sudoku, it uses only the numbers 1 through 9, and numbers cannot be repeated in subrows or sub columns.  You might notice that the black boxes are sometimes separated by diagonal lines.  The numbers in a subrow must add up to the number above the diagonal in the black box on left of the subrow; the numbers in a sub column must add up to the number below the diagonal in the black box on top of the sub column.

Unique number combinations are very important in Kakuro.  Consider the number 4 over 2 squares: the only combination permitted in Kakuro would be 1 and 3, since 2 and 2 would be repeating a number.  In the bottom righthand corner of the puzzle in Figure 1, for instance, we know that a 1 must go in the bottom, righthand-most box since the column has to add up to 3 (with the unique combination 1 and 2) and the row has to add up to 4 (with the unique combination 1 and 3).

The single digit rule is also very important.  Consider the square below the 5 in the rightmost column of Figure 1, in the same row with the 13.  Now, 5 can be either 2 and 3 or 1 and 4, but whatever goes in the square also has to work with 13.  If we put 1, 2, or 3 in that box, we would have to put a double-digit number in the other box to make 13.  Thus only a 4 can go there.

One last trick is to consider the minimum and maximum numbers that can be made over a series of squares.  For instance, the highest number we can make over 4 squares is 30 (9 + 8 + 7 + 6).  If we’re trying to make the number 33 over 5 squares, we know we can’t use 2 or 1, because then we would have to be able to make 32 or 31 over 4 squares.  Minimums works in a similar way: if we’re trying to make 11 over 3 squares, we can’t use 9, because then we’d have to make 2 over 2 squares, which is impossible.  The smallest number we can make over 2 squares is 3 (1 + 2).

Kakuro is much more complex than Sudoku, and, if I may say so, much more interesting.  I hope you will give it a try.  Below is a link to online puzzles.  Happy puzzling!

http://www.kakuroconquest.com

___________________________________________________________________

Sources:

http://www.conceptispuzzles.com/index.aspx?uri=puzzle/kakuro/history

My roommate’s best friend Bryce enjoys Kakuro on a daily basis.  People are always asking him, “Bryce, why do you love Kakuro so much?” and he says, “Oh, I don’t know, I’m just clowning around.”