Given that in the city of London the number of inhabitants is greater than the number of hairs on the head of any one of them, and that none of them is bald, can we suppose that there must be at least two inhabitants with the exact same number of hairs on their head?
A trial is being held for two men accuses of murder. The jury finds one of them guilty and the other not guilty. The judge turns to the guilty one and says "this is the strangest case I've ever seen. Although there's absolutely no doubt of your guilt, the law obliges me to release you with no charges.
How can you explain this?
THE SMITH ROBBERY
A robbery has taken place at the Smiths house. There are three suspects: William Roberts, Thomas Jones and Peter Cullpepper. The detective in charge of the case knows that Thomas never lies, that William always lies and that Peter sometimes lies and sometimes says the truth. Under questioning, the three declared as follows:
William: "I confess, I did it!"
Thomas: "Peter isn't guilty!"
Peter: "William's the culprit!"
Who is the guilty party?
JOHN'S FOUR SONS
John is the proud father of four handsome boys. The eldest is four years older than the second, who is in turn four years older than the third, who is four years older than the youngest. The youngest is half as old as the eldest.
What are the ages of each of John's sons?
ANOTHER HAIR-RAISING TALE
A variation on the same problem: In York these three things are true:
A. None of the residents have exactly the same number of hairs.
B. None of them has exactly 518 hairs.
C. There are more residents than hairs on the head of any one resident.
You've got two buckets of water. The water in the first bucket is 15º Celsius, and in the second 15º Fahrenheit. If you drop a stone into both buckets, in which of the two will the stone fall to the bottom of the bucket?