Some of the ‘brain teaser’ puzzles doing the rounds at the moment annoy me. The problem is that if you don’t know the parameters on which the question is posed, you can’t get the ‘right’ answer.
Take the one involving apples (10 points each), bananas and coconuts. Depending on how you read it, a banana was worth either 4 points (as a bunch, irrespective of the number in the bunch) or 1 per banana, which meant the number in the bunch counted. Coconuts were 1 per half, but the ambiguity over the banana meant that it was impossible to come up with a single ‘correct’ answer. And some people interpreted the split coconut as less than half (I think it’s perspective, but who can really tell?).
The ‘correct’ answer, I believe, was to consider bananas as individuals – but that was ambiguous, because they were connected as a bunch. How do you handle that? No instructions given.
The nature of reality is, of course, that it is fuzzy and we spend a lot of time trying to nail down the un-nailable, because (in western society particularly) we are conditioned to look for ‘one’ answer, the ‘right’ answer.
However, that isn’t a metaphor for the ‘brain teasers’ which, instead, rely on incomplete parameters – we aren’t given the full information needed to solve the problem in the way we’re being asked to – which gets us tangled in knots trying to find that ‘right’ answer (and argue over it) when in fact there isn’t one.
The actual answer to the apple puzzle is not a number, but a logic expression that accounts for the ambiguity:
LET an apple be 10, and IF bananas are treated as a bunch, LET their value be 4; OR if bananas are treated singly, LET their value be 1, and in all cases, LET a half-coconut be 1.
If you do the arithmetic, the answer is EITHER 15 OR 14. And that, technically, is perfectly OK. Sometimes, answers have to be expressed as a number range, or with margins of error.
However, this kind of answer isn’t the one being asked for when the question is posed, and THAT is why I get annoyed, because the question and the required answer don’t match – it’s a trick in which those answering the question get misled by ambiguity.
Needless to say, this same logic trap also dogs IQ tests. The classic is the ‘missing house component’ problem that confronted Eastern European migrants trying to enter the US via Ellis Island in the 1920s. They had to sit an IQ test to prove they were smart enough to become Americans. Faced with a house missing a part, they drew in the one important to them: a crucifix above the door. By US standards, the house was missing a chimney, thus proving that Eastern Europeans were stupid people.
Actually, of course, the morons were the ones who set the test and then believed that it actually measured anything valid, but that’s the power of early twentieth century structuralism for you.
Copyright © Matthew Wright 2016