Crack Puzzles

At one point, a remote island’s population of chameleons was divided as follows:
- 13 red chameleons
- 15 green chameleons
- 17 blue chameleons
Each time two different colored chameleons would meet, they would change their color to the third one. (i.e.. If green meets red, they both change their color to blue.) Is it ever possible for all chameleons to become the same color? Why or why not?”

A man has two children. He says one of them is a son. What is the probability that the other one is also a son?

line of 100 airline passengers is waiting to board a plane. they each hold a ticket to one of the 100 seats on that flight. (for convenience, let’s say that the nth passenger in line has a ticket for the seat number n.)
Unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. all of the other passengers are quite normal, and will go to their proper seat unless it is already occupied. if it is occupied, they will then find a free seat to sit in, at random.
What is the probability that the last (100th) person to board the plane will sit in his proper seat (#100)?

You are on a rowboat in the middle of a large, perfectly circular lake. On the perimeter of the lake is a monster who wants to eat you, but fortunately, he can’t swim. He can run (along the perimeter) exactly 4x as fast as you can row, and he will always run towards the closest bit of shore to your boat. If two paths take him to this location equally quickly, he will arbitrarily choose one. If you can touch shore even for a second without the monster already being upon you, you can escape. The monster can reverse direction instantaneously and you can turn your boat instantaneously. Suggest a strategy that will allow you to escape, and prove that it works.

This one is a simple algorithm question.
There are ‘n’ numbers. Maximum of the ‘n’ numbers can be found in (n-1) comparisons, similarly minimum can be found in (n-1) comparisons. In total there would be (2n-2) comparisons. Can you find out the maximum & minimum in lesser number of comparisons?