Three friends, Alice, Bob, and Charlie, each own a special coin. These coins are unique in that:
One coin is always heads.
One coin is always tails.
One coin flips randomly, landing on heads or tails with equal probability.
The friends met up and decided to play a game. Each person flipped their coin, and then they all revealed the results. Here's what they said:
Alice: "I don't know what's going on, but at least one of our coins must be the randomly flipping one."
Bob: "Mine's definitely not the one that always lands on heads."
Charlie: "I can tell you that Bob and I have different results."
Can you determine who owns which coin?
Let's analyze each statement:
Alice says that at least one of the coins must be the randomly flipping one. This means that Alice cannot have the coin that always lands on the same side. If Alice had that coin, she would know the outcome in advance. Therefore, Alice must have either the coin that always lands on heads or the one that flips randomly.
Bob says that his coin is not the one that always lands on heads. So, Bob cannot have the coin that always lands on heads. This means Bob either has the coin that flips randomly or the one that always lands on tails.
Charlie says that he and Bob have different results. This implies that Charlie does not have the coin that always lands on the same side as Bob. So, Charlie cannot have the coin that always lands on tails.
From these statements, we can conclude:
Alice cannot have the coin that always lands on heads.
Bob cannot have the coin that always lands on heads, and he cannot have the coin that always lands on tails.
Charlie cannot have the coin that always lands on tails.
Therefore, Alice must have the coin that flips randomly.
Now, let's determine who has the coins that always land on heads and tails:
Bob cannot have the coin that always lands on heads, so Charlie must have it.
Therefore, Bob must have the coin that always lands on tails.
So, the final conclusion is:
Alice has the coin that flips randomly.
Bob has the coin that always lands on tails.
Charlie has the coin that always lands on heads.
