Question 12
Xavier,Ylenia and Zoe sometimes play the lottery. They want to learn whether someone won while keeping the winner's identity secret. Each pair meets and tosses a coin together. Each person announces whether their two observed tosses were the same or different. Everyone tells the truth except the winner, who lies. The example shows Zoe winning and all three announcing “different”.
In the example the Zoe–Xavier toss is tails, Xavier–Ylenia is heads, and Zoe–Ylenia is tails. Now Xavier announces “same”, Ylenia “same”, Zoe “different”, and at most one person won. Who won?
In the example the Zoe–Xavier toss is tails, Xavier–Ylenia is heads, and Zoe–Ylenia is tails. Now Xavier announces “same”, Ylenia “same”, Zoe “different”, and at most one person won. Who won?