2019 AMC 12B Problems/Problem 23

Revision as of 11:36, 14 February 2019 by Magentacobra (talk | contribs) (Solution)

Problem

Solution

We can deduce that any valid sequence of length $n$ wil start with a 0 followed by either "10" or "110". Because of this, we can define a recursive function:

$f(n) = f(n-3) + f(n-2)$

This is because for any valid sequence of length $n$, you can remove either the last 2 numbers ("10) or the last three numbers ("110") and the sequence would still satisfy the given conditions.

Since f(5) = 1 and f(6) = 2, you build up until $f(19) = 65 \boxed{C}$

See Also

2019 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 22
Followed by
Problem 24
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All AMC 12 Problems and Solutions
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