sums from 1 to a, first reaching b wins, first player without winning strategy
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2018 Shortlist LRP1 (Logic Reasoning Probability)
October 2, 2021
combinatoricsgamegame strategywinning strategy
Problem Statement
Arnulfo and Berenice play the following game: One of the two starts by writing a number from to , the other chooses a number from to and adds it to the initial number, the first player chooses a number from to and adds it to the previous result, they continue doing the same until someone manages to add . When Arnulfo was about to start, Berenice told him that it was unfair, because whoever started had a winning strategy, so the numbers had better change. So they asked the following question:
Adding chosen numbers from to , until reaching the number , what conditions must meet and so that the first player does not have a winning strategy?
Indicate if Arnulfo and Berenice are right and answer the question asked by them.