100 ruble notes for buying books
Source: Tournament of Towns, Junior A-Level , Fall 2019 p6
April 20, 2020
combinatorics
Problem Statement
Peter has several ruble notes and no other money. He starts buying books; each book costs a positive integer number of rubles, and he gets change in ruble coins. Whenever Peter is buying an expensive book for rubles or higher he uses only ruble notes in the minimum necessary number. Whenever he is buying a cheap one (for less than rubles) he uses his coins if he has enough, otherwise using a ruble note.
When the ruble notes have come to the end, Peter has expended exactly a half of his money. Is it possible that he has expended rubles or more? (Tatiana Kazitsina)