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| ==Problem==
| | #REDIRECT[[2019_AMC_10B_Problems/Problem_25]] |
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| ==Solution==
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| We can deduce that any valid sequence of length <math>n</math> wil start with a 0 followed by either "10" or "110".
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| Because of this, we can define a recursive function:
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| <math>f(n) = f(n-3) + f(n-2)</math>
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| This is because for any valid sequence of length <math>n</math>, you can remove either the last two numbers ("10") or the last three numbers ("110") and the sequence would still satisfy the given conditions.
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| Since <math>f(5) = 1</math> and <math>f(6) = 2</math>, you follow the recursion up until <math>f(19) = 65 \quad \boxed{C}</math>
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| -Solution by MagentaCobra
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| ==See Also==
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| {{AMC12 box|year=2019|ab=B|num-b=22|num-a=24}}
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