Postman Problem: Max 10 Delivering to 19 Houses

[lilhaz]

Suppose there's a single terraced street that contains 19 houses. The postman notices that no 2 adjacent houses ever receive mail on the same day, and that no more than 2 adjacent houses don't receive mail on any day. What is the maximum number of days he can deliver before repeating the pattern?

The Attempt at a Solution

well, there are a maximum of 10 deliveries he can make, starting at house 1 then missing a house and delivering to house 3 etc. And he can make a minimum of 6 deliveries
There is only 1 way to deliver to 10 houses, but after that my methods start to fall apart! anyone got any insight that can help?

 

[lippyka]

The maximum number of days he can deliver before repeating the pattern is 18 days. On the first day, he can deliver to houses 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19. On the second day, he can deliver to houses 2, 4, 6, 8, 10, 12, 14, 16, and 18. After this, he can repeat the pattern.