Consider 2009 cards which are lying in sequence on a table
Source: VAIMO 4, German Pre-TST 2010
July 16, 2011
combinatorics unsolvedcombinatoricsgame strategy
Problem Statement
Consider 2009 cards which are lying in sequence on a table. Initially, all cards have their top face white and bottom face black. The cards are enumerated from 1 to 2009. Two players, Amir and Ercole, make alternating moves, with Amir starting. Each move consists of a player choosing a card with the number such that whose top face is white, and then this player turns all cards at positions The last player who can make a legal move wins.(a) Does the game necessarily end?
(b) Does there exist a winning strategy for the starting player?Also compare shortlist 2009, combinatorics problem C1.