Thursday, August 13, 2009

NPR Puzzle -- 08/09/09 What Is the Exchange Rate Between the Rial & the Lira?

Here's this week's puzzle, from the Aristotle's Diner series :

A waitress walks up to a breakfast table with five logicians and asks, "Does everyone here want coffee?"

The first logician says, "I don't know."

The second logician says, "I don't know."

The third logician says, "I don't know."

The fourth logician says, "I don't know."

And the fifth logician says, "No."

Who did the waitress bring coffee to — and why?

The answer is that the waitress brings each of the first four logicians coffee, and no coffee for the fifth. The way to think about this is that the only way the answer to her question is Yes is if all five of them want coffee. As soon as any one of them doesn't want coffee, the answer is then No.

So Logician #1 knows he wants coffee, but doesn't know if any of his compatriots do, so he says he doesn't know -- it could be they all want coffee (answer = Yes), or it could be that one or more do not (Answer = No).

Logician #2 knows he wants coffee, and he can deduce that L#1 does as well, but Ls#3-5 are as yet unknown entities, coffee-wise, so he also says "I don't know."

L#3 and L#4 are the same as L#1 and L#2 -- each knows he/she wants coffee, and that all the logicians thus far want coffee, but it could still be the case that one of the last logicians (or the very last logician, in L#4's analysis) does not want coffee, so the answer could still be either yes or no.

L#5 gets all this. She or he can tell that Ls#1-4 all want coffee, so it comes down to L#5's preference -- if yes for coffee, then yes to the waitress's question. If no coffee, then the answer is no.

And now for the analogies (and Will, if you're reading this -- don't do these again, okay? Darn near made my head explode):

1. Hibiscus is to bird as benevolent is to MAMMAL (or RODENT)

2. Drain is to Serbia as rail is to ITALY (or IRAN)

3. Ride is to sin as had is to COUNTRY (or FISH)

Alt. 3. Ride is to sin as race is to VIRTUE

4. Family is to Peru as Victoria Cross is to EGYPT

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