Problem

Source: 1998 Estonia National Olympiad Final Round grade 10 p3

Tags: combinatorics



The hotel has $13$ rooms with rooms from $1$ to $13$, located on one side of a straight corridor in ascending order of numbers. During the tourist season, which lasts from May $1$st to October $1$st, the hotel visitor has the opportunity to rent either one room for two days in a row, or two adjacent rooms together for one day. How much could a hotel owner earn in a season if it is known that on October $1$, rooms $1$ and $13$ were empty, and the payment for one room was one tugrik per day?