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determine the number of elements

Source: Ireland 1997

July 3, 2009
combinatorics unsolvedcombinatorics

Problem Statement

Let S S be the set of natural numbers n n satisfying the following conditions: (i) (i) n n has 1000 1000 digits, (ii) (ii) all the digits of n n are odd, and (iii) (iii) any two adjacent digits of n n differ by 2 2. Determine the number of elements of S S.
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