.Both A and B Alice and Bob play the following
chip-off-the-table game. Given a pile of 58 chips, Alice
first picks at least one chip but not all the chips. In
subsequent turns, a player picks at least one chip but no
more than the number picked on the previous turn by the
opponent. The player to pick the last chip wins. Which of
the following is true?
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Answer Posted / Khushboo Srivastava
To solve this problem, let's analyze the possible moves for both players:
1. Alice starts by picking 1 chip.
2. Bob picks at least 1 chip (let's say he picks x chips). Now, Alice must pick at least one but not more than x chips.
3. Bob picks at most x chips again.
4. This process repeats until the last chip is picked.
Since Alice can only pick up to the number of chips that Bob picked in the previous round, she will always pick one fewer chip than Bob in each subsequent turn. Thus, Bob will win the game.
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