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So if we have (say on the first place) a x in the one pattern and a 1 in the other, the intersection will have a 1 at this place. The only new thing is, that when patterns clash with a 1 and 0, we set this to 3 which means something like both.

So if we have (say on the first place) a x in the one pattern and a 1 in the other, the intersection will have a 1 at this place. The only new thing is, that when patterns clash with a 1 and 0, we set this to 3 which means something like both, 0 and 1 appeared.

The reason for this is that the intersection of those patterns is not empty. They both have the same combinations in it and therefore, we have to take care to subtract them only once. This intersection argument remembered me of the Inclusion-exclusion principle because we basically want the same: We want to count the number of the union of a set of forbidden patterns.

The reason for this is that the intersection of those patterns is not empty. They both have the same combinations in it and therefore, we have to take care to subtract them only once. This intersection argument remembered me of the Inclusion-exclusion principle because we basically want the same: We want to count the number of elements in the union of a set of forbidden patterns.

or the examples with 5000 digits

or the examples with 5000 digits which belisarius used to time the operation