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BEBRAS 2019 Grade 9-10 Round 2 Ext Question 10

BEBRAS · BEBRAS 2019 Grade 9-10 Round 2 Ext

Question 10

Xavier,Ylenia and Zoe want to reveal whether someone won the lottery while keeping the winner’s identity secret. Each pair meets and tosses one coin. Each person announces whether the two tosses they participated in were the same or different. Everyone tells the truth except a winner, who gives the opposite answer. In this example Zoe won and all announce “different”; Úp and Ngửa label the two coin faces.

Question illustration

Now Xavier says “same”, Ylenia says “same”, and Zoe says “different”. At most one person won. Who is the winner?
  1. Xavier
  2. Ylenia
  3. Zoe certainly did not win
  4. Someone certainly won, but their identity cannot be determined