[Math4u] A Combinatorial Problem

Solving the following problem with pencil and paper is possible, though
a bit tedious. You may want to write a small computer program in the
language of your choice - it is probably easier and much more fun, too!

So here is the problem. Consider pairs of consecutive integers in the
set S = {10000 <= n <= 19999, n ε N}. Some of these, such as (11110,
11111), have elements that can be added together without requiring a
carry. Others, such as (19998, 19999), have elements that require
carrying when they are added together.

Question: For how many such pairs of consecutive integers from S is no
carrying required when the two integers are added together?

In the unlikely case that nobody comes up with the correct answer, I'll
post a solution next year. :-)

Michael

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