Difference between revisions of "2019 AMC 12B Problems/Problem 23"

Latest revision as of 12:27, 14 February 2019

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-==Problem==
+#REDIRECT[[2019_AMC_10B_Problems/Problem_25]]
-==Solution==
-We can deduce that any valid sequence of length <math>n</math> wil start with a 0 followed by either "10" or "110".
-Because of this, we can define a recursive function:
-<math>f(n) = f(n-3) + f(n-2)</math>
-This is because for any valid sequence of length <math>n</math>, 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 <math>f(19) = 65 \boxed{C}</math>
-==See Also==
-{{AMC12 box|year=2019|ab=B|num-b=22|num-a=24}}