What does Christopher tell Mrs Alexander?

Mrs Alexander knew about Christopher's mother's affair, but not about her 'death'.

In the same conversation when she tells Christopher about the affair, he tells her that his mother died. She was shocked to hear this, but she took Christopher's word for it. Perhaps she'd known her neighbours well enough to know about the affair (or perhaps she'd heard about that through gossip from other neighbours who knew them better), but she probably assumed that Christopher's mother had gone away with Mr Shears and she simply hadn't heard about her death. Perhaps the affair was common knowledge in the neighbourhood, and Mrs Alexander assumed that the death was something less talked about (scandal always makes for better gossip than tragedy).

After all, if the lie about Christopher's mother's death was good enough to fool Christopher himself - her own son, and a boy with a shrewd and enquiring mind - surely it can't have been something that a neighbour who didn't know the family very well could have seen through.

Then she sucked in another big breath and said, “Because... because I think you know why your father doesn’t like Mr. Shears very much.” Then I asked, “Did Mr. Shears kill Mother?” And Mrs. Alexander said, “Kill her?” And I said, “Yes. Did he kill Mother?” And Mrs. Alexander said, “No. No. Of course he didn’t kill your mother.” And I said, “But did he give her stress so that she died of a heart attack?” And Mrs. Alexander said, “I honestly don’t know what you’re talking about, Christopher.” And I said, “Or did he hurt her so that she had to go into hospital?” And Mrs. Alexander said, “Did she have to go into hospital?” And I said, “Yes. And it wasn’t very serious at first, but she had a heart attack when she was in hospital.” And Mrs. Alexander said, “Oh my goodness.”

I said, “And she died.”

And Mrs. Alexander said “Oh my goodness” again, and then she said, “Oh, Christopher, I am so, so sorry. I never realized.” Then I asked her, “Why did you say ‘I think you know why your father doesn’t like Mr. Shears very much’?” Mrs. Alexander put her hand over her mouth and said, “Oh dear, dear, dear.” But she didn’t answer my question. So I asked her the same question again, because in a murder mystery novel when someone doesn’t want to answer a question it is because they are trying to keep a secret or trying to stop someone from getting into trouble, which means that the answers to those questions are the most important answers of all, and that is why the detective has to put that person under pressure. But Mrs. Alexander still didn’t answer. Instead she asked me a question. She said, “So you don’t know?”

And I said, “Don’t know what?”

[...]

And she said, “I shouldn’t have said what I said. And if I don’t explain, you’ll carry on wondering what I meant. And you might ask your father. And I don’t want you to do that because I don’t want you to upset him. So I’m going to explain why I said what I said. But before I do that you have to promise not to tell anyone I said this to you.” I asked, “Why?” And she said, “Christopher, please, just trust me.” And I said, “I promise.” Because if Mrs. Alexander told me who killed Wellington, or she told me that Mr. Shears had really killed Mother, I could still go to the police and tell them because you are allowed to break a promise if someone has committed a crime and you know about it.

And Mrs. Alexander said, “Your mother, before she died, was very good friends with Mr. Shears.”

And I said, “I know.” And she said, “No, Christopher. I’m not sure that you do. I mean that they were very good friends. Very, very good friends.” I thought about this for a while and said, “Do you mean that they were doing sex?”

And Mrs. Alexander said, “Yes, Christopher. That is what I mean.”

-- Chapter '97' (emphasis mine)

After having two Black Days in a row, Christopher saw five red cars on his way to school, which meant this day will be a Super Good Day. He must wait until school is out to find out what the Super Good Day holds for him. This day it is meeting Mrs. Alexander in a shop, where Christopher is buying some candy. Mrs. Alexander asks Christopher why he left before she could serve him tea and biscuits the other day. He tells her he was afraid she would call the police on him for investigating Wellington's death. Outside the shop, Christopher notices Mrs. Alexander's dog, Ivor, and makes friends with him. Mrs. Alexander and Christopher begin to talk about Christopher's love of computers and maths. He tells her he is going to take the A level maths, which impresses her very much. He thinks that since they are getting along it wouldn't hurt to ask her if she knows any information about Mr. Shears. He feels this is not breaking his promise to his father, because he is not asking about Wellington and he is not saying Mr. Shears name at home. Mrs. Alexander tells Christopher his father probably doesn't like Mr. Shears. Christopher wants to know if Mr. Shears is responsible for putting so much stress on his mother that she had a heart attack and died. Mrs. Alexander is stunned by the news that Christopher's mother is dead. She asks Christopher to take a walk with her in the park. Christopher is reluctant, because he doesn't like the park, which has people who inject themselves with illegal drugs in it. He is also afraid to go into the park with Mrs. Alexander as he considers her a stranger, but in the interest of finding more out about Mr. Shears and Wellington, he accompanies her into the park. She begins by telling Christopher he cannot repeat anything she says to his father. He promises to not tell his father, so she continues on by telling Christopher Mr. Shears and his mother were very close friends. At first Christopher takes her literally and doesn't understand what she is trying to tell him. Then he asks her if they had sex and she tells him they did, which is why Mr. and Mrs. Shears no longer live together and Christopher's father hates Mr. Shears. Christopher, after hearing the news, decides to go home. Mrs. Alexander reminds him of his promise and tells him he can talk to her anytime he needs to.

Mr. Jeavons, the school psychologist, tells Christopher the reason he likes maths is because the problems have a logical answer, which is different from life. But Christopher thinks Mr. Jeavons doesn't understand maths, because there isn't always a logical answer. This is illustrated by the The Monty Hall Problem, which in essence states if given three doors to choose from, one of which contains a valuable prize, a contestant should change their choice of doors after being shown what is behind one of the doors. This is because then the contestant has a 2 in 3 chance of getting the valuable prize if they change their pick, instead of the fifty/fifty chance most people think is possible. Christopher likes this example, because it shows math is not straight forward like most people think it is.

Christopher is fascinated with Sherlock Holmes stories, especially The Hounds of the Baskervilles. He feels he is in some ways like Sherlock Holmes, because he too looks for the logical explanation of situations and he likes the clues and red herrings in the story. He also feels if he becomes a detective it would be a detective like Sherlock Holmes.