In a game called Card Nim, each player has a collection of cards, each with a number on it. In each turn a player reveals a card and removes a number of stones equal to the number on the card. To win on a move, a player must play a card whose number is equal to the number of stones remaining. To lose on a move, a player plays a card whose number is greater than the number of stones remaining.
Warm-Up: Suppose there are five stones left and each of the two players Bob and Alice has three cards with 1, 2, and 3, respectively. Alice goes first. Who wins?
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