Five stickers, three friends, one deduction

Question

A teacher has five stickers: three green and two yellow. She sticks one on the forehead of each of three friends, Ravi, Sana, and Tim, and hides the two leftover stickers. Nobody can see their own sticker. They are seated so that Ravi sees both Sana's and Tim's foreheads, Sana sees only Tim's, and Tim sees no one. All three are perfect logicians and answer honestly, one at a time: - Ravi: "I can't tell what color my sticker is." - Sana: "Neither can I." - Tim: "Then I know mine." What color is Tim's sticker, and how does he know?

Accepted Answer

Work through the three remarks in order. Ravi speaks. He sees Sana and Tim. There are only two yellow stickers in the whole set. If Ravi saw two yellow foreheads in front of him, both yellows would be accounted for, and his own would have to be green, he'd know instantly. Since Ravi says he can't tell, Sana and Tim are not both yellow. (At most one of them is yellow.) Sana speaks. She heard Ravi, so she also knows Sana-and-Tim aren't both yellow. She can see Tim. If Tim's sticker were yellow, then, since she and Tim can't both be yellow, Sana's own would have to be green, and she'd know it. B…

Five stickers, three friends, one deduction

Your answer

More Brainteasers questions