## Postal Worker

A postal worker has $600$ houses on his route. During one snowy day, he noticed that every other house’s mailbox was blocked by snow, and he could not deliver the mail. He also noticed that he had no mail to deliver to every third house on the route. By the end of his route, how many households had mail that was still in his truck?
Source: NCTM Mathematics Teacher 2008

SOLUTION
Suppose there are $18$ households on the route.

B = blocked by snow
N = no mail
Number of households that have no mail, $18\div 3=6$, namely $\{3, 6, 9, 12, 15, 18\}$.
Number of households that have mail, $18-6=12$, namely {1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17}.
Half of the $12$ households having mail are blocked by snow; the mail of $6$ households is still in his truck.
Number of households that have no mail, $600\div 3=200$.
Number of households that have mail, $600-200=400$.
Half of the $400$ households having mail are blocked by snow; the mail of $200$ households is still in his truck.

Answer: $200$