Do you prefer jam or treacle?
Source: 43rd International Tournament of Towns, Junior A-Level P7 & Senior A-Level P6, Fall 2021 & Kvant Magazine No. 11-12 2021
February 18, 2023
combinatoricsTournament of TownsKvant
Problem Statement
There are 20 buns with jam and 20 buns with treacle arranged in a row in random order. Alice and Bob take in turn a bun from any end of the row. Alice starts, and wants to finally obtain 10 buns of each type; Bob tries to prevent this. Is it true for any order of the buns that Alice can win no matter what are the actions of Bob?Alexandr Gribalko