Can you name the ten countries of the world whose names are only four letters long?
See the comments for the answer.
Consider three types of people in a medieval kingdom - Knights, Knaves, and Normals. Knights always tell the truth, Knaves always lie, and Normals can do either. The King wants his daughter to marry a nice normal Normal, not one of those goody-goody Knights or devious scoundrel Knaves.
For a (much) harder twist, suppose the King doesn’t trust those unpredictable Normals and wants his daughter to marry a Knight or a Knave instead.
This puzzle can be found in it’s original form in Raymond Smullyan’s What is the Name of This Book? although this slightly modified version is taken from the excellent [wu:riddles].
Over the last couple of weeks I’ve been reading Joseph Heller’s classic Catch-22, which I’m currently about halfway through. An FT quote on the back of the book reads: “Blessedly, monstrously, bloatedly, cynically funny, and fantastically unique.” I wasn’t sure what that meant until I started reading the book, but it’s now clear to me that the description is indeed very accurate. Take, for example, the following passage which is typical of Heller’s cynically funny style throughout the whole book so far:
“From now on,” he said, “I don’t want anyone to come in to see me while I’m here. Is that clear?”
“Yes, sir,” said Sergeant Towser. “Does that include me?”
“Yes.”
“I see. Will that be all.”
“Yes.”
“What shall I say to the people who do come to see you while you’re here?”
“Tell them I’m in and ask them to wait.”
“Yes, sir. For how long?”
“Until I’ve left.”
“And then what shall I do with them?”
“I don’t care.”
“May I send them in to see you after you’ve left?”
“Yes.”
“But you won’t be here then, will you?”
“No.”
“Yes, sir. Will that be all?”
“Yes.”
“Yes, sir.”
“From now on,” Major Major said to the middle-aged enlisted man who took care of his trailer, “I don’t want you to come here while I’m here to ask me if there’s anything you can do for me. It that clear?”
“Yes, sir,” said the orderly. “When should I come here to find out if there’s anything you want me to do for you?”
“When I’m not here.”
“Yes, sir. And what should I do?”
“Whatever I tell you to.”
“But you won’t be here to tell me. Will you?”
“No.”
“Then what should I do?”
“Whatever has to be done.”
“Yes, sir”
“That will be all,” said Major Major.
“Yes, sir,” said the orderly. “Will that be all?”
“No,” said Major Major.
I’d certainly recommend it so far.
The answer is surprisingly simple. If at any stage somebody sits in your seat (number 50), then you will inevitably be forced to sit elsewhere. Similarly, if at any stage somebody sits in seat number 1, then each subsequent person will have their seat available and so you will end up sitting in your own seat. Now at each stage, while seats 1 and 50 are free, there is an equal chance of a person choosing to sit in seat 1 as seat 50. Hence, your chance of sitting in your own seat is a half.
You’re taking a coach trip up to Scotland and are standing in line waiting to board the coach as it prepares to depart from London. There are 50 seats on the coach and each passenger standing in line is assigned one of these seats (for simplicity, suppose they are lined up in order with the first person in line being assigned to seat number 1, etc). Now the first passenger in line is horribly drunk and randomly chooses a seat. The subsequent passengers are all sober and so they’ll sit in their allocated seat if it’s free. If not, they’ll choose one at random to sit in. If you’re at the very back of the line, what are the chances of you sitting in your allotted seat (number 50) when you eventually get to board?
