Kakuro Instructions
A kakuro puzzle will look like the one below, but of course bigger:
Each kakuro puzzle is composed of a number of rows and columns, some cells are empty and light coloured, others some have numbers in them. At first look therefore it looks like a crossword.
Every sequence of cells in either a row or a column is called a 'run'. At the left of each horizontal run, and at the top of each vertical run, you will see a number.
In the image above, you can see, for instance, a '5' in the second cell on the top row. This means simply that the sum of the two cells underneath it is 5. Next to the '5' is '21'  this means, therefore, that the three cells underneath it sum to 21. And so on, throughout the puzzle.
Using this information alone, you can solve a kakuro puzzle. The key constraint is that you can only use a number once in each run. Therefore if you need to make '6' from two numbers, you cannot use '3' twice, but must rather use 1 and 5 or 4 and 2. You may only use the numbers 1 to 9.
Kakuro Hints
Here are a few hints to help you solve the puzzles:
 Try to look at the lowest value and highest value small runs first. That's because these have the lowest possible combinations (for instance '17' from two cells can only be 8 and 9 or 9 and 8.
 Look for common numbers between runs at the point they intersect. For instance, if two runs that intersect only have a 4 in common, that must be the number at the intersection
 Practice a lot and learn combinations of numbers for each sum
 Use pencilmarks to note down possible remaining values for a cell
 Each time you place another number, work back through to find the implications for the rest of the puzzle
 Remember all puzzles have one unique solution
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