Kakuro Puzzle

Hello,
This game is similar to crossword game that there is a grid of cells but instead of playing with letters to form a word, you're going to play with numbers from 1 to 9.
Your task is to fill all empty cells with numbers as long as sum of them equals to a specified number and is satisfied with one condition: do not repeat the same number.
Let look at this example: 4 = 1 + 3 or 3 + 1 is valid; but 4 = 2 + 2 is not allowed because the number 2 used two times.