Logic Masters Deutschland e.V.

In the first part we drew simple conclusions from the numbers in the puzzle. Now we introduce a new kind of conclusion, that we can draw from the numbers. Assume the following situation:

It is easy to see, that the for red marked cells do not belong to the ones. The reason is that the two blue marked cells each contribute one diagonal to each of the ones. Analogous in the following example, we can draw four diagonals.

This kind of conclusion can be generalized. We assume a chain of numbers (that is a group of numbers without a gap, that all lie within one column or row). Die inner cells each belong to exactly one of the numbers. With the sum of the numbers, we can calculate the number of outer diagonals, that belong to the chain. In the example we have 6 inner cells and the sum of the numbers is 6. Thus none of the outer cells belongs to the chain.

When the difference between the number of inner cells and the sum of the number is 0 or 4, we can completely fill out the outer fields. Very often we also find chains with a difference between 0 and 4. In these cases, we cannot directly draw in diagonals, but later in the puzzle, we can draw conclusions, as soon as some of the outer cells are filled. In the following figure, a couple of examples are shown. The puzzle boundary can also be used in chains.

Useful chains always have twos in the middle.

The following puzzle can be solved using chains and the techniques from the first part.