A curious book

In the novel from Mark Haddon "The Curious Incident of the Dog in the Night-Time" the main character is a 15 years-old autistic child that discovers the corpse of his neighbors' dog in the frontyard. ¿Who could have committed this horrible crime?

This book is fascinating, and its chapters, labeled with prime numbers, alternate between the main plot and a description of the image of the world the main character has.

A brief extract, translating from chapter 67 (that is number 19):

Talking to strangers is not something I usually do. I do not like talking to strangers. This is not because of the Stranger Danger which they tell us about at school, which is where a strange man offers you sweets or a ride in his car because he wants to do sex with you. I am not worried about that. If a strange man touched me I would hit him, and I can hi people very hard. For example, when I punched Sarah because she had pulled my hair I knocked her unconcious and she had a concussion and they had to take her to the Accident and Emergency Department at the hospital. And also I always have my Swiss Army Knife in my pocket and it has a saw blade which could cut a man's finger off.

The main character of the book is a kid that has a strong interest in physics and mathematics. For the same reason it includes, parallel to the main plot, the description of some classic math problems. One example is the following: you are in a contest in television and there are three doors: A, B, and C. Behind one of the doors there is a car. Behind the other two doors there is a goat. You have to pick one door to open, and we will assume you prefer the car.

You pick door A, but before opening it, the presenter of the program opens door C and shows that there is a goat behind it. He offers you the possibility of keeping door A that you chose originally, or change to door B. ¿What should you do?. Most people, including people that has studied a lot of mathematics, thinks that it's equal to stay in A or to change to B.

Actually, the best strategy is to change to B. The argument goes as follows. Let's suppose the goats are called goat 1 and goat 2. At the beginning you choose a door at random. With probability 1/3 you picked the car, with probability 1/3 goat 1, and with probability 1/3 goat 2.

• If you originally picked the car, then changing is bad.
• If you originally picked goat 1, then the presenter showed you goat 2, and changing is good.
• If you originally picked goat 2, then the presenter showed you goat 1, and changing is good.

So, 2 out of 3 times it is better to change, so changing door is better than staying in the current door. There is more information about the puzzles in this book in a review at the Mathematical Association of America.