The Curious Incident of the Dog in the Night-Time (27 page)

And you had to detach the top part of the puzzle from the bottom part, and it was really difficult.

And another good thing was that I helped Mother paint her room
White with a Hint of Wheat,
except I got paint in my hair and she wanted to wash it out by rubbing shampoo on my head when I was in the bath, but I wouldn't let her, so there was paint in my hair for 5 days and then I cut it out with a pair of scissors.

But there were more bad things than good things.

And one of them was that Mother didn't get back from work till 5:30 p.m. so I had to go to Father's house between 3:49 p.m. and 5:30 p.m., because I wasn't allowed to be on my own and Mother said I didn't have a choice, so I pushed the bed against the door in case Father tried to come in. And sometimes he tried to talk to me through the door, but I didn't answer him. And sometimes I heard him sitting on the floor outside the door quietly for a long time.

And another bad thing was that Toby died because he was 2 years and 7 months old, which is very old for a rat, and I said I wanted to bury him, but Mother didn't have a garden, so I buried him in a big plastic pot of earth like a pot you put a plant in. And I said I wanted another rat but Mother said I couldn't have one because the room was too small.

And I solved the puzzle because I worked out that there were two bolts inside the puzzle and they were tunnels with metal rods in them like this

And you had to hold the puzzle so that both rods slid to the end of their tunnels and they weren't crossing the intersection between the two pieces of the puzzle and then you could pull them apart.

And Mother picked me up from Father's house one day after she had finished work and Father said, “Christopher, can I have a talk with you?”

And I said, “No.”

And Mother said, “It's OK. I'll be here.”

And I said, “I don't want to talk to Father.”

And Father said, “I'll do you a deal.” And he was holding the kitchen timer, which is a big plastic tomato sliced through the middle, and he twisted it and it started ticking. And he said, “Five minutes, OK? That's all. Then you can go.”

So I sat on the sofa and he sat on the armchair and Mother was in the hallway and Father said, “Christopher, look . . . Things can't go on like this. I don't know about you, but
this . . . this just hurts too much. You being in the house but refusing to talk to me . . . You have to learn to trust me . . . And I don't care how long it takes . . . If it's a minute one day and two minutes the next and three minutes the next and it takes years I don't care. Because this is important. This is more important than anything else.”

And then he tore a little strip of skin away from the side of the thumbnail on his left hand.

And then he said, “Let's call it . . . let's call it a project. A project we have to do together. You have to spend more time with me. And I . . . I have to show you that you can trust me. And it will be difficult at first because . . . because it's a difficult project. But it will get better. I promise.”

Then he rubbed the sides of his forehead with his fingertips, and he said, “You don't have to say anything, not right now. You just have to think about it. And, um . . . I've got you a present. To show you that I really mean what I say. And to say sorry. And because . . . well, you'll see what I mean.”

Then he got out of the armchair and he walked over to the kitchen door and opened it and there was a big cardboard box on the floor and there was a blanket in it and he bent down and put his hands inside the box and he took a little sandy-colored dog out.

Then he came back through and gave me the dog. And he said, “He's two months old. And he's a golden retriever.”

And the dog sat in my lap and I stroked it.

And no one said anything for a while.

Then Father said, “Christopher, I would never, ever do anything to hurt you.”

Then no one said anything.

Then Mother came into the room and said, “You won't be able to take him away with you, I'm afraid. The bed-sit's too small. But your father's going to look after him here. And you can come and take him out for walks whenever you want.”

And I said, “Does he have a name?”

And Father said, “No. You can decide what to call him.”

And the dog chewed my finger.

And then it was 5 minutes and the tomato alarm went. So Mother and I drove back to her room.

And the next week there was a lightning storm and the lightning hit a big tree in the park near Father's house and knocked it down and men came and cut the branches up with chain saws and carried the logs away on a lorry, and all that was left was a big black pointed stump made of carbonized wood.

And I got the results of my maths A level and I got an A grade, which is the best result, and it made me feel like this

And I called the dog Sandy. And Father bought him a collar and a lead and I was allowed to take him for walks to the shop and back. And I played with him with a rubber bone.

And Mother got flu and I had to spend three days with Father and stay in his house. But it was OK because Sandy slept on my bed so he would bark if anyone came into the room during the night. And Father made a vegetable patch in the garden and I helped him. And we planted carrots and peas and spinach and I'm going to pick them and eat them when they're ready.

And I went to a bookshop with Mother and I bought a book called
Further Maths for A Level
and Father told Mrs. Gascoyne that I was going to take A-level further maths next year and she said “OK.”

And I am going to pass it and get an A grade. And in two years' time I am going to take A-level physics and get an A grade.

And then, when I've done that, I am going to go to university in another town. And it doesn't have to be in London because I don't like London and there are universities in lots of places and not all of them are in big cities. And I can live in a flat with a garden and a proper toilet. And I can take Sandy and my books and my computer.

And then I will get a First Class Honors degree and I will become a scientist.

And I know I can do this because I went to London on my own, and because I solved the mystery of
Who Killed Wellington?
and I found my mother and I was brave and I wrote a book and that means I can do anything.

A
PPENDIX

QUESTION

Prove the following result:

A triangle with sides that can be written in the form
n
²
+ 1,
n
²
- 1 and 2
n
(where
n
> 1) is right-angled.

Show, by means of a counterexample, that the converse is false.

ANSWER

First we must determine which is the longest side of a triangle with sides that can be written in the form
n
²
+ 1, n
²
- 1
and
2n
(where
n > 1
)

n
²
+ 1 - 2n = (n - 1)
²

and if
n > 1
then
(n - 1)
²
> 0

therefore
n
²
+ 1 - 2n > 0

therefore
n
²
+ 1 > 2n

Similarly
(n
²
+ 1) - (n
²
- 1) = 2

therefore
n
²
+ 1 > n
²
- 1

This means that
n
²
+ 1
is the longest side of a triangle with sides that can be written in the form
n
²
+ 1, n
²
- 1
and
2n
(where
n > 1
).

This can also be shown by means of the following graph (but this doesn't prove anything):

According to Pythagoras's theorem, if the sum of the squares of the two shorter sides equals the square of the hypotenuse, then the triangle is right-angled. Therefore to prove that the triangle is right-angled we need to show that this is the case.

The sum of the squares of the shorter two sides is
(
n
²
- 1)
²
+ (2
n
)
²

(
n
²
- 1)
²
+ (2
n
)
²
= n
⁴
- 2
n
²
+ 1
+ 4
n
²
=
n
⁴
+ 2
n
²
+ 1

The square of the hypotenuse is
(
n
²
+ 1)
²

(
n
²
+ 1)
²
=
n
⁴
+ 2
n
²
+ 1

Therefore the sum of the squares of the shorter two sides is equal to the square of the hypotenuse and the triangle is right-angled.

And the converse of “A triangle with sides that can be written in the form
n
²
+ 1,
n
²
- 1
and
2
n
(where
n
> 1
) is right-angled” is “A triangle that is right-angled has sides whose lengths can be written in the form
n
²
+ 1,
n
²
- 1
and
2
n
(where
n
> 1
).”

And a counterexample means finding a triangle which is right-angled but whose sides cannot be written in the form
n
²
+ 1,
n
²
- 1
and
2
n
(where
n
> 1
).

So let the hypotenuse of the right-angled triangle
ABC
be
AB.

and let
AB = 65

and let
BC = 60

Then
CA = √ (AB
²
- BC
²
)

= √ (65
²
- 60
²
) = √ (4225 - 3600) = √ 625 = 25

Let
AB =
n
²
+ 1 = 65

then
n = √ (65 - 1) = √ 64 = 8

therefore
(
n
²
- 1) = 64 - 1 = 63 ≠ BC = 60 ≠ CA = 25

and
2n = 16 ≠ BC = 60 ≠ CA = 25

Therefore the triangle
ABC
is right-angled but it does not have sides which can be written in the form
n
²
+ 1,
n
²
- 1
and
2
n
(where
n
> 1
).
QED