IrMO 1997 P2 Q4: Upper Secondary Mathematics Competition Question

Let S be the set of all natural numbers n satisfying the following conditions:

(i) n has 1000 digits;

(ii) all the digits of n are odd, and

(iii) the absolute value of the difference between adjacent digits of n is 2.

Determine the number of distinct elements in S.

[Irish MO (IrMO) 1997 Paper 2 Q4]

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