Race to 32.768!

Logic Level 3

Alice and Bob play a game with the following rules:

  • There are 9 cards on a table with the numbers: \(2,4,8,16,32,64,128,256,512\)
  • In each turn a player pick exactly one card.
  • Whoever gathers 3 cards with a product of \(32768\) wins.
  • Both players play optimally.
  • Alice starts first.

Question: Which player has a winning strategy?

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