IMO 2010 Shortlist C4
Six stacks S1,...,S6 of coins are standing in a row. In the beginning every stack contains a single coin. There are two ...
Category: Combinatorics
Problem
Six stacks S1,...,S6 of coins are standing in a row. In the beginning every stack contains a single coin. There are two types of allowed moves: Move 1: If stack Sk with 1 ¨k ¨5 contains at least one coin, you may remove one coin from Sk and add two coins to Sk 1. Move 2: If stack Sk with 1 ¨ k ¨ 4 contains at least one coin, then you may remove one coin from Sk and exchange stacks Sk 1 and Sk 2. Decide whether it is possible to achieve by a sequence of such moves that the first five stacks are empty, whereas the sixth stack S6 contains exactly 201020102010 coins.