Something to get your logical teeth into…

I’m very interested in maths. Or rather I used to be. I’m taking a holiday for the moment.

Many of the mathematical problems in Curious Incident were given to me by my good friend, Dave Cohen.

I would solve each one, have a few weeks off, then ask for another.

Christopher’s obsession with maths therefore allowed me to indulge a minor obsession of my own. I made a mistake, however, by including the infamous Monty Hall Problem in the novel[1]. Since the novel was published, I have received several hundred letters pointing out, often over many pages and in great detail, how Christopher (and I) had got the answer wrong[2]. I hadn’t. The problem is famous precisely because the answer is so infuriatingly counter-intuitive. Initially, I replied at length, expanding on the solutions given in the novel. I urged correspondents to mock up a version of the game themselves with matchboxes and coins. I suggested they played the game with a friend on a rainy Sunday afternoon, maybe even placing money on the outcome and seeing whether Christopher’s tactics or their own made a profit. The letters kept on coming. My replies grew shorter. I became a little terse on occasions (particularly with one man who worked for the National Institutes for Statistics, or somesuch, who said that he was going to be lecturing in schools, using my novel as an example of how even intelligent people got maths completely wrong).

My interest in puzzles began to wane, and I haven’t been back to Dave for another for over a year now. But I can’t resist sharing one of my favourites. Like all the best puzzles it seems quite obviously insoluble.

People who don’t like maths, look away now…

A mathematician goes to a party with her husband (Dave always likes to add a feminist tweak to his puzzles). There are five other couples at the party. Introductions are made and hands are shaken, to a greater or lesser extent (no-one shakes hands with themselves, of course, nor with their partners; and no-one shakes another persons’ hands twice). Later on during the party the mathematician asks everyone (including her own husband) how many people’s hands they’ve shaken. She gets 11 answers, all of them different. That is, she gets every answer from 0 to 10.

How many hands did she herself shake?

If you work this out without using a piece of paper I will be mightily impressed. If you do resort to a piece of paper make it a big one.

I’ll give you the answer in a subsequent entry.

[1]Some relief was afforded by a smaller numbers of letters agreeing with me (and Christopher), thanking me for solutions the writers didn’t know, and sometimes offering different, elegant solutions of their own.
[2]See Coming Down the Mountain.