MathDB
a hotel has 13 rooms

Source: 1998 Estonia National Olympiad Final Round grade 10 p3

November 4, 2020
combinatorics

Problem Statement

The hotel has 1313 rooms with rooms from 11 to 1313, located on one side of a straight corridor in ascending order of numbers. During the tourist season, which lasts from May 11st to October 11st, 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 11, rooms 11 and 1313 were empty, and the payment for one room was one tugrik per day?