by Erik Setser

Created on: June 12, 2009

What happens when you leave sudoku and crosswords alone in a dark room for a few hours with a little champagne and some mood music? After however long their gestation period is, you'd have a bouncing baby kakuro puzzle.

Kakuro is great for anybody who enjoys sudoku but is looking for something different, something a bit more challenging. And challenging it is, indeed! These puzzles can be quite daunting for the first-timer, what with every white cell being empty. Those converting from sudoku to kakuro are likely accustomed to starter clues. Well, the black squares hold all the clues we need.

Around the edges of the white squares are black squares with diagonal lines running from the top left to the bottom right. A number to the right of the line is a row number, while one to the left is a column number. Using any or all digits from 1 to 9 with no repeats, the cells in a row must have a sum equal to the row number and those in a column to the column number. For instance, the number 8 split over two cells (henceforth denoted as 8|2) can be 7 and 1, 6 and 2, or 5 and 3, but not 4 and 4. Get it? The answers are all there, sitting in those row and column numbers. It's all just a matter of how we use them, and getting the most out of them is two parts logic, one part clever trickery. The best place to start is with unique sums

Every kakuro book has a list of unique sums. A unique sum is a row or column number that has only one possible combination of cell numbers. These include the highest, lowest, second highest and second lowest possible sums for each size. With practice, these can be memorized, their recollection becoming second nature. But here's a list for reference in the meantime:

(3|2 = 1,2 4|2 = 1,3 17|2 = 9,8 16|2 = 9,7) (6|3 = 1,2,3 7|3 = 1,2,4 24|3 = 9,8,7 23|3 = 9,8,6) (10|4 = 1,2,3,4 11|4 = 1,2,3,5 30|4 = 9,8,7,6 29|4 = 9,8,7,5) (15|5 = 1,2,3,4,5 16|5 = 1,2,3,4,6 35|5 = 9,8,7,6,5 34|5 = 9,8,7,6,4) (21|6 = 1,2,3,4,5,6 22|6 = 1,2,3,4,5,7 39|6 = 9,8,7,6,5,4 38|6 = 9,8,7,6,5,3) (28|7 = 1,2,3,4,5,6,7 29|7 = 1,2,3,4,5,6,8 42|7 = 9,8,7,6,5,4,3 41|7 = 9,8,7,6,5,4,2)

Any possible sum over 8 cells (ranging from 36 to 44) is unique since only one number is left out. Just subtract the sum from 45 to figure out what's missing. Similarly, a row or column with 9 cells will invariably add up to 45 and thus include every one-digit number once. If you see a puzzle that breaks this rule, you have a dud.

To get started, skim around for unique sums, focusing

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