Thursday, 31 January 2013

Chopping logic

These are twins. The one on our left is older.
I have had an interesting discussion with Paul Nahin, the author of The Logician and the Engineer, which I'm currently reading to review.

Nahin quotes a logic problem that is apparently well known amongst mathematicians. In it, one person is trying to guess the (integer) ages of the other's three daughters. He is given some information that allows him to narrow the possible ages down 1, 6 and 6 or 2, 2, and  9. Then the first gives an additional pieces of information. 'My oldest daughter,' he says, 'likes bananas.' Immediately the second person knows the girls' ages.

The accepted correct solution goes that the daughters can't be 1, 6 and 6 because there isn't an oldest daughter in this scenario, so our logician can deduce they are 2, 2 and 9. But I say that this is rubbish - at the very least poor logic.

Why? It is perfectly possible to have two six-year-old daughters born 10 months apart. Clearly one is older than the other. However even with twins, one is always older than the other for legal reasons. 

Prof. Nahin counters with two points. One is that integer ages were specified, and the other than this is a pure maths problem so legality doesn't enter into it.

I would say it doesn't matter about the 'integer' ages bit - both daughters have the integer age of six in both my counter examples. (And even if they literally had to be six that day, they could still be twins). As for the 'pure maths problem' argument, that doesn't hold up either. This clearly isn't a pure maths problem. It features a person liking bananas. Pure maths? I think not. It is an attempt to apply logic to a (admittedly rather odd) real world situation. In the real world it would be perfectly acceptable for the father to comment about his 'oldest daughter' even if the six-year-olds were twins, because she is accepted as such. As a father of twin daughters, I have done this.

If logic is being applied to a real world problem, I'd suggest it should take into account the way that the real world describes things.

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