Welcome to the Kakuro Challenge!
Kakuro is the next fiendishly addictive and absorbing puzzle to
come of out Japan, where hundreds of dedicated puzzle masters devote
their lives to working out ways to reduce your productivity down
to zero, and we guarantee— if you liked Sudoku, you're going
to love Kakuro!
The Kakuro Challenge 1 by Alastair Chisholm contains over
two hundred Kakuro puzzles, in four levels. They start with some
easy Delicious introductory puzzles, and then work up through Pernicious,
Malicious, and finally the hideously eye-watering Vicious.
What is Kakuro?
Kakuro is sometimes described as a "number crossword".
This is an example puzzle:
The puzzle is made up of blocks of white squares, running either
in a row or a column. For example, along the top of the puzzle is
a block of three white squares. To solve the puzzle, you have to
fill in all the white squares, following these three rules:
You can only use the numbers 1 to 9.
The numbers in each block must add up to the Target (the small
number at the left of each row and the top of each column).
Each block can only contain each number once.
...And that's all there is. How hard can it be? The great thing
about Kakuro is that, like Sudoku, there's only one solution, and
you never have to guess (thought you might be tempted!)/ And once
you've mastered the Vicious Kakuro puzzles in The Kakuro Challenge
1 and 2, you can hold your head up with the pride that comes with
knowing you can solve puzzles that are just as fiendish as Sudoku,
and you can count!
How To Solve Kakuro Puzzles
The best way to learn how to solve Kakuro puzzles is to actually
solve them, and here we'll take the first puzzle and work through
every step: 
Although
it's a simple example, the techniques you learn here will help you
with every Kakuro puzzle you ever come across. Here goes!
Combinations
Kakuro puzzles are all about Combinations. For example,
in the puzzle above, look at the block leading from C3. It has
five squares, and the Target is 32 (that's known as "32 in 5".
What combinations can fit?
Remember, a number can't appear twice in the same block—so
for example
9+8+7+4+4=32
Although it adds up to 32, it uses the 4 twice—no good. The
valid combinations are:
9+8+7+6+2=32
9+8+7+5+3=32
9+8+6+5+4=32
How does this help us? And even if we knew the right
combination of numbers, how can we work out the right order? Relax,
and remember—you
never have to guess.
32-in-5 is no use to us—too many combinations and possibilities
to worry about. What we need is to find something a bit more useful.
And fortunately these things exist, and we call them Kakuro Blocks.
For more information on Kakuro Blocks, see The
Kakuro Challenge 1 and The
Kakuro Challenge 2 by Alastair Chisholm available
wherever puzzle books are sold. Have fun!
Here are a random sampling of puzzles in several of these categories.
Just download and play!