succession of positive integers of $2006$ terms, 2 player game
Source: Argentina 2006 OMA L3 p3
May 12, 2024
combinatoricsnumber theory
Problem Statement
Pablo and Nacho write together a succession of positive integers of terms, according to the following rules: Pablo begins, who in his first turn writes , and from then on, each one in his turn writes an integer positive that is greater than or equal to the last number that the opponent wrote and less than or equal to triple the last number that the opponent wrote. When the two of them have written the numbers, the sum of the first numbers written (all except the last one) and the sum of the numbers written. If and are co-cousins, Nacho wins. Otherwise, Pablo wins. Determine which of the two players has a winning strategy, describe the strategy and demonstrate that it is a winning one.