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Link of the day: Blue Eyes: a logic puzzle. I don't think it's the hardest in the world, but it is kinda tricky.
Actually, the puzzle reminds me of a story I read in a popular mathematics magazine once.
(Note: I am retelling the story as fiction. It was presented in the magazine as an actual anecdote in first person, but as, first, I don't remember the details (up to and including whether the narrator was male or female), and second, it's a little 'too good to be true'....)
Our Hero, henceforth referred to as Mary for reasons surely unrelated to Hal Clement's "Still River", has just gotten her PhD, and is looking for a position. One day, after interviewing at one of her candidate schools, she gets invited to an 'informal holiday party' at the university president's house to meet the faculty. She, of course, attends.
The first thing she notices is that, despite the 'informal', everyone is wearing their Sunday best, so to speak. As she is in her street clothes, this puts something of a damper on her spirits. Worse is the near-impenetrable conversational block between her and the other people there. As a result of this, she is wallflowering by the refreshments table with a drink in her hand – and has been for about four drinks – when the host announces a party game.
The crowd is divided into three groups, and the university president describes the rules. Each group will stand in a corner of the room with a card, either red or white. They will hold the card so they can't see which color it is, but both other groups can. Then, everyone who can see a white card raises their hand. The goal, the president explains, is to figure out what color your group's card is.
They then move to their respective corners, Mary following her group. She watches as the President has one member of each group hold the card facing the ground. On cue, everyone holds up their cards, and she sees that both other groups have white cards. She raises her hand. So do everyone else.
Well, that tells me nothing, she thinks. They can each see each others' white cards, so of course they'll raise their hands. And she stands off to the side as everyone begins huddling to discuss the solution.
Ten minutes pass. No-one has ventured a guess.
Twenty minutes. People are beginning to get a little irritable, but the president is going around encouraging them to keep trying.
Thirty minutes. Mary begins going over the problem in her head again, ignoring the other group members. What if our group had a red card? she thinks. What would the other groups see?
A red card and a white card, of course. And everyone holding up their hands.
She starts. That's it! Why would the group with the white card be holding up their hands? If we had a red card, they'd know they had a white one! We must have a white card!
Excited now, Mary checks over her logic again. If we have a red card, that implies the others see a red card and a white card. If they saw a red card and white card, they would know they have a white card, because the people with the white card can't see their own card, and the other one's red. But neither of them have solved the problem, so we must therefore have a white card.
It's brilliant, she realizes. Give every group white cards. They're all stuck until they start looking at it from the perspective of the others. It's the ultimate lateral-thinking exercise – the president must have been planning this the whole time – just brilliant... She checks her logic again. It's flawless. She stands up.
"I got it," she says, triumphantly. All eyes turn to her. She begins to explain her logic, point by point, speaking faster and faster and more and more enthusiastically as she approaches her conclusion.
"And so, therefore," she yells, wrapping up, "either the lot of you are complete idiots, or this card is white!" And, as everyone stares, she grabs the card and turns it around.
It's red.
Actually, the puzzle reminds me of a story I read in a popular mathematics magazine once.
(Note: I am retelling the story as fiction. It was presented in the magazine as an actual anecdote in first person, but as, first, I don't remember the details (up to and including whether the narrator was male or female), and second, it's a little 'too good to be true'....)
Our Hero, henceforth referred to as Mary for reasons surely unrelated to Hal Clement's "Still River", has just gotten her PhD, and is looking for a position. One day, after interviewing at one of her candidate schools, she gets invited to an 'informal holiday party' at the university president's house to meet the faculty. She, of course, attends.
The first thing she notices is that, despite the 'informal', everyone is wearing their Sunday best, so to speak. As she is in her street clothes, this puts something of a damper on her spirits. Worse is the near-impenetrable conversational block between her and the other people there. As a result of this, she is wallflowering by the refreshments table with a drink in her hand – and has been for about four drinks – when the host announces a party game.
The crowd is divided into three groups, and the university president describes the rules. Each group will stand in a corner of the room with a card, either red or white. They will hold the card so they can't see which color it is, but both other groups can. Then, everyone who can see a white card raises their hand. The goal, the president explains, is to figure out what color your group's card is.
They then move to their respective corners, Mary following her group. She watches as the President has one member of each group hold the card facing the ground. On cue, everyone holds up their cards, and she sees that both other groups have white cards. She raises her hand. So do everyone else.
Well, that tells me nothing, she thinks. They can each see each others' white cards, so of course they'll raise their hands. And she stands off to the side as everyone begins huddling to discuss the solution.
Ten minutes pass. No-one has ventured a guess.
Twenty minutes. People are beginning to get a little irritable, but the president is going around encouraging them to keep trying.
Thirty minutes. Mary begins going over the problem in her head again, ignoring the other group members. What if our group had a red card? she thinks. What would the other groups see?
A red card and a white card, of course. And everyone holding up their hands.
She starts. That's it! Why would the group with the white card be holding up their hands? If we had a red card, they'd know they had a white one! We must have a white card!
Excited now, Mary checks over her logic again. If we have a red card, that implies the others see a red card and a white card. If they saw a red card and white card, they would know they have a white card, because the people with the white card can't see their own card, and the other one's red. But neither of them have solved the problem, so we must therefore have a white card.
It's brilliant, she realizes. Give every group white cards. They're all stuck until they start looking at it from the perspective of the others. It's the ultimate lateral-thinking exercise – the president must have been planning this the whole time – just brilliant... She checks her logic again. It's flawless. She stands up.
"I got it," she says, triumphantly. All eyes turn to her. She begins to explain her logic, point by point, speaking faster and faster and more and more enthusiastically as she approaches her conclusion.
"And so, therefore," she yells, wrapping up, "either the lot of you are complete idiots, or this card is white!" And, as everyone stares, she grabs the card and turns it around.
It's red.