2001 AIME I Problems/Problem 14

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Problem

A mail carrier delivers mail to the nineteen houses on the east side of Elm Street. The carrier notices that no two adjacent houses ever get mail on the same day, but that there are never more than two houses in a row that get no mail on the same day. How many different patterns of mail delivery are possible?


Therefore, the number of $19$-digit strings is $a_{19}+b_{19}+c_{19} = 86+151+114 = \boxed{351}.$

See also

2001 AIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 13
Followed by
Problem 15
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All AIME Problems and Solutions

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