Making a Start
Let's look at a real kakuro. Where do you start? Well, before we commence entering lots of candidate numbers there is an important rule to learn. We have already learned that there are some fixed combinations of numbers, such as 3 in two = 1 and 2, 4 in two = 1 and 3. If two of these blocks intersect and share a unique number then the point where they intersect must be that common number. If we examine the puzzle, there are quite a few of these fixed combinations:

• 3 in two = 1, 2
• 4 in two = 1, 3
• 7 in three = 1, 2, 4
• 16 in five = 1, 2, 3, 4, 6

Are there any combinations that intersect and share a unique digit? Yes, look at the bottom row of Figure 1. Here the 4 intersects with the 3 in the central black square. They both share the number 1 uniquely, so that must be the number that goes in the cell that they both share. Before we move on to find some more of these, it is important to remember that they must share the number uniquely. For example, the 16 intersects with the top 4, but they both contain 1 and 3, so the cell at the intersection could be either 1 or 3 (but that fact may in itself be a help later on).

Back at our puzzle there are two more places where 3 and 4 intersect (Figure 2), so both of the intersecting cells resolve to 1. Having solved those three squares directly, there are now some holes that can be filled as a result (Figure 3).

Next: Reducing combinations