Art, the mail carrier delivers mail to the 19 houses on the east side of a street.

Art notices that:
(i) No two adjacent houses ever get mail on the same day, and:
(ii) There are never more than two houses in a row that get no mail on the same day.

How many distinct patterns of mail delivery are possible?

(In reply to re(2): a manua etc............. thank you by Ady TZIDON)

One of the things I love about math, and about this site in particular, is the way we  are able to come up with three or four different approaches to solving the same problem.  And all the approaches prove that the other approaches are valid also.  That's a lot of validation.  Well done, all.

Posted by Steve Herman on 2014-09-05 08:48:51