After Sudoku now Kakuro wins popularity. Kakuro puzzles exist already for a long time. I found them in a Dutch magazine and in some puzzle books with different kind of puzzles. The difference between Sudoku and Kakuro is that for Kakuro you need to do some math. Sudoku with numbers is the most easy way to solve Sudoku’s, with images or letters Sudoku becomes more difficult to solve for the human brain.
The quickest way to solve Kakuro is
1. Use the basic Kakuro rules to assign possibilities to each square. You need a list of the combinations that make up a clue. For example 3 in 2 is (1,2), 4 in 2 is (1,3), 5 in 2 (1,4),(2,3), 6 in 2 (1,5,2,4) etc.
When the clues cross take the intersection of the sets. So if 5 in 2 crosses 6 in 2, the possibilities for that square are 1,2,4, the only common values.
2. Consider each clue as set of possibilities. It might go (123,56) on an 8 in 2 clue. However, the only combinations that make 8 are (2,6),(3,5) so the 1 is not a possibility and should be removed from the set of possibilities.
By using the intersection of the sets of possibilities in each square (8 in 2 crossing a 5 in 2 for example (1,2,3)), then by taking the set of possibilities for each clue (the possibilities of each square), and identifying which possibilities in the set are not possible to make the sum of the clue, the entire puzzle can be solved.
UPDATE: More techniques for solving Kakuro Puzzles can be found at passion for puzzles strategy page for solving Kakuro Puzzles.
You can buy Kakuro at Amazon.