Kakuro has been hailed as the worthy successor to sudoku, the puzzle craze that swept the world in 2005.

If you thought sudoku was the greatest puzzle to hit the planet since crosswords, then here's another of those sometimes infuriating but always entertaining number puzzles popularized in Japan. It is said that in that country kakuro is more popular than sudoku.

Kakuro is a hybrid of logic puzzle and number crossword. The clues are the sums of the digits in each block of numbers. All you have to do is work out where the digits from one to nine should go.

The puzzles in The Penguin Book of Ultimate Kakuro will provide you with a mental tussle that may take only a few minutes or keep you occupied for an hour or more. Don't be deceived by the size of the grid-a small one can be just as tough as a large one. All puzzles in this book have an indication of the level of difficulty.

A short, illustrated tutorial will start you off on the road to a new puzzle addiction.

To Solve Kakuro:

Kakuro is a hybrid of a crossword and a logic puzzle. Like a crossword, kakuro has across and down clues—only instead of phrases, it's numbers. The object of the puzzle is to fill the blank cells with numbers between 1 and 9 that produce a sum which equals the clue... Make sense?
 
The clues are the numbers printed on the black squares--above the white diagonal line are the across clues and below it are the down clues. The clues are the sum of the solution block (the blank cells) next to the clue. Thus, if a 3 is shown as a clue there will be two empty cells waiting for you to put the digits 1 and 2 in them—the only possible sum that will equal 3... Still with me?
 
The final rule is that no number may be repeated in any block. For example, if the clue is 4, the only possible solution will be 1 and 3 (or 3 and 1), never 2 and 2. Therefore, no matter how large the grid is, the longest block will be 9 cells in length to accommodate the digits 1 to 9.

To summarize...

The clue represents the sum of the numbers in the adjacent block of empty cells.
 
The numbers 1-9 are used to fill the grid
 
Each block may contain only one occurrence of a digit