Rodolfo and Gabriela play with 9 numbered chips
Source: I May Olympiad (Olimpiada de Mayo) 1995 L1 P3
September 17, 2022
combinatoricsgamegame strategywinning strategy
Problem Statement
Rodolfo and Gabriela have chips numbered from to and they have fun with the following game: They remove the chips one by one and alternately (until they have chips each), with the following rules:
Rodolfo begins the game, choosing a chip and in the following moves he must remove, each time, a chip three units greater than the last chip drawn by Gabriela.
Gabriela, on her turn, chooses a first chip and in the following times she must draw, each time, a chip two units smaller than the last chip that she herself drew.
The game is won by whoever gets the highest number by adding up their three tokens.
If the game cannot be completed, a tie is declared.
If they play without making mistakes, how should Rodolfo play to be sure he doesn't lose?