How to Solve a kakuro logic puzzle

Kakuro puzzles are logic puzzles found in many newspapers. They are similar to Sudoku puzzles in that you fill in numbers as the solution. They are very addictive and use simple addition. Here is an instruction to help you along.

Difficulty: Moderate

Instructions

1. The solutions to the Kakuro puzzle add up to the clues. The numbers in each row (horizontal) add up to the clue on the left of that row. A whole column has to add up to the clue at the top of the column. You can use all digits 1-9, but no number can repeat itself in a single row or column. For instance a clue of "4" can be 1-3, but it cannot be 2-2.

2. Write down this key that includes a lot of the numbers that have only one solution:
   
   Number of spaces-1-----2-------3-------4-------5-------6------7-------8------9
   Counting Down------9----17-----24-----30-----35-----39-----42-----44-----45
   Counting Up----------1-----3------6------10-----15------21-----28-----36-----45

3. 
    

   Scan the puzzle looking for these clues first. Fill in as many as you can so that you have other numbers to work off of. Also look for clues that are 1 less or 1 more. For example, 3 spaces with the clue of 23 can only be 9-8-6, and 3 spaces with 7 as a clue can only be 1-2-4.

4. 
    

   Use both the horizontal and vertical numbers as clues. For instance at the at the top left, 17 down has only 2 spaces, so 9 and 8 are the only numbers that work (see the chart above) And since there is a 9 across with 2 spaces, that one has to be filled in with the 8 because 1 is the smallest number you can use in the other space.

5. 
    

   And when you look at the 38 across, there are 6 spaces so it can only be 9-8-7-6-5-3. The 3 digit 6 down can only 6 down can only be 1-2-3 so where they intersect is a 3 since that is the only number that can be in both. And the 2 digit, 4 across right above it can only be a 1-3. Since we already used the 3 for the 6 down, where the 6 down and the 4 across intersect must be a 1. Then you can fill in the remaining digits of both 6 down and 4 across.

6. 
    

   As for the remainder of the 38 across, we have already used the 9 and the 3 leaving 8-7-6-5 for the rest. 5 is now the only one that matches the 15 down (1-2-3-4-5). After that, 6 is the only one that will work with 7 down (making the other space 1). After that 8 is the only number that will work for 23 down (9-8-6) and then 7 is all that is left.

7. 
    

   After that sometimes you have to resort to trial and error. Try to find a spot with as few possibilities as possible. Look at where the 15 down and 12 across intersect. 1 and 2 don't work at all. If you put in a 5 and work it through to the right you find that it won't work. So it must be the 3. Work it through filling in the 9, then 6, then 1. Now only 2 and 5 are left to fill in. We already have a 2 and a 5 in each row so it is easy to fill them in.

8. 
    

   I can talk through the rest of the puzzle, but that would get pretty boring and now that you have the basic overview I'm sure you can so them yourself. Just in case you are curious here is a finished puzzle. The small number in the bottom is the order in which I filled them in.