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Riddles ------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------ Bright Women Four extremely bright women are at a party. The hostess takes a set of eight stickers, 4 yellow and 4 purple, and shows the stickers to the other three women. She then puts two stickers on the forehead of each woman. Everyone can see all the other stickers except the two in the hostess' pocket and the two on her own head. The hostess asks each woman in turn if she knows the colors of her own stickers. The answer as follows: Alice: "No" Brenda: "No" Cyndi: "No" Alice: "No Brenda: "Yes" What are the colors of Brenda's stickers, and how did she figure it out? (Figure that at each step, the women all gave the only possible answer and that their reasoning was correct.) Solution: Brenda had one yellow and one purple sticker on her forehead. At this point it is unknown what the colors were on the other two women's foreheads. Brenda reasons: "If I have two purple stickers, Alice would have figured out her colors on her second turn. Brenda figures Alice's reasoning would be: 'Brenda has two purple stickers. If I (Alice) also have two purple stickers, then all four purples would be used, and Cyndi would have known that she had two yellow stickers. However, Cyndi didn't say she had two yellow stickers, so I don't have two purple stickers.' Alice would have also figured, if I (Alice) have two yellow stickers, then Cyndi would have realized that if she had two purple stickers, I would have seen four purples and I would have answered that I had two yellow stickers on my first turn. On the other hand, if Cyndi has two yellow stickers, then Brenda would have seen four yellows and she would have answered that she had two purples. Therefore Cyndi would have realized that, if I (Alice) have two yellow stickers and Brenda has two purple stickers, and if neither of us answered on our first turn, then she (Cyndi) must have one yellow and one purple sticker. (Of course, Alice can see Cyndi’s stickers, but this reasoning is included to show the complete logic.) "'But Cyndi didn't say she had one yellow and one purple. So I (Alice) can't have two yellow stickers either. If I can't have two yellow or two purple stickers, then I must have one yellow and one purple sticker.' Brenda's reasoning continues: "Alice didn't say that she had one yellow and one purple sticker, so the supposition that I have two purple stickers must be wrong. And as my logic applies to yellow-yellow as well, then I must have one yellow and one purple sticker." |
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