Soluciones:

A HAIR RAISING TALE

Yes. Let us suppose that there are 8 million residents in London. If each resident had a
different number of hairs on his head, there would have o be 8 million positive, whole
number under 8 million, and that is impossible!

DOUBLE JEOPARDY

The accused were Siamese twins

THE SMITH ROBBERY

Thomas

JOHN'S FOUR SONS

The eldest is 24, the second is 20, the third is 16 and the youngest is 12.

ANOTHER HAIR RAISING TALE

518. Suppose that there are more than 518 residents, for example 520. There then would
have to exist 520 different numbers all less than 520 and none equal to 518. This is not
possible. There are exactly 520 different numbers (including 0) less than 520, and
therefore only 519 numbers less than 520 that are not 518.

TWO BUCKETS

In the bucket containing the water at 15º Celsius, because the water in the other bucket
is frozen solid.