3. Consider the game of piles played by two players player 1 and player 2. The...

 

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3. Consider the game of "piles" played by two players player 1 and player 2. The game starts with 50 jellybeans split evenly into two piles each of 25. Each turn consists of the active player taking a positive number of jellybeans from a single pile, then passing the turn. Player 1 takes the first turn. The person who takes the last jellybean wins. A winning strategy for player 2 is to always leave the piles for player one so that each pile has the same number of jellybeans. If at any point one of the piles is empty then player 2 can take the remaining jellybeans from the other pile. Use strong induction to prove that this strategy will win every time. (In other words, prove the claim that for any integer b such that b 0, if there are b beans in each pile to start, then Player 2 has a winning strategy.) 3. Consider the game of "piles" played by two players player 1 and player 2. The game starts with 50 jellybeans split evenly into two piles each of 25. Each turn consists of the active player taking a positive number of jellybeans from a single pile, then passing the turn. Player 1 takes the first turn. The person who takes the last jellybean wins. A winning strategy for player 2 is to always leave the piles for player one so that each pile has the same number of jellybeans. If at any point one of the piles is empty then player 2 can take the remaining jellybeans from the other pile. Use strong induction to prove that this strategy will win every time. (In other words, prove the claim that for any integer b such that b 0, if there are b beans in each pile to start, then Player 2 has a winning strategy.)

Answer rating: 100% (QA)

Answer Base Case When there are 0 jellybeans in each pile to start b 0 Player 2 has a winning strate... View the full answer