MathDB

2

Part of 2011 Argentina National Olympiad

Problems(1)

winning strategy for 2 pleayers tema up aginaast third on, piles of stones

Source: 2011 Argentina OMA Finals L3 p2

1/15/2023
Three players A,BA,B and CC take turns removing stones from a pile of NN stones. They move in the order A,B,C,A,B,C,…AA,B,C,A,B,C,…A. The game begins, and the one who takes out the last stone loses the game. The players AA and CC team up against BB , they agree on a joint strategy. BB can take in each play 1,2,3,41,2,3,4 or 55 stones, while AA and CC, they can each get 1,21,2 or 33 stones each turn. Determine for what values ​​of NN have winning strategy AA and CC, and for what values ​​the winning strategy is from BB. .
combinatoricsgamegame strategywinning strategy