#### 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.

Just saying.

*Copyright © Matthew Wright 2016*

Yeah that is exactly why I do not like IQ tests, never took one but saw so many “teasers” which are just like that, so stupid.

They work by misleading – they don’t actually state a soluble question and then people get tangled trying to get that solution. In this case, the pictures are ambiguous and therefore their actual numeric value cannot be identified. People argue over the definitions and miss the point that an ‘ambiguous’ answer – stating a range of values drawn from the available range of possibilities – is actually also correct and acceptable.

Yup

I came up with 15.

3x=30,

x=10 ———–(1)

10+2y=18

2y=8

y=4 ————(2)

4-z=2

z=2 ————–(3)

z+x+y= 16

yes, that’s what I got too. I can’t see how it can be anything else. 😦

Yes, if Z is also defined as “any piece of coconut, part or half”. Or alternatively:

3x = 30 therefore x = 10

10 + 2y = 18 therefore y = 4

4 – Z = 2 therefore Z = 2

But what is not defined is whether Y is comprised of 1 x 4 individual items or counts as a single item. As algebra the puzzle above becomes 1/2Z + X + 3Y = N OR 1/2Z + X + 1Y = N – and plugging in the values obtained above N becomes either 14 or 15.

That’s another way to look at it

Huh. I got 16 )))

I figured “apple picture = 10”, “bananas picture = 4”, “coconuts picture = 2”. I didn’t even notice there was a different number of bananas and coconut halves. Because, in that case, how the heck does an apple stand for 10? Ten what? Apple seeds? Worms inside? ))

Good point about the tests!

I did the same as you, and also hand’t noticed the different number of bananas in a bunch, Then when Matthew started describing that a coconut = 1, I actually got more confused. As there’s no symbol between the two coconut halves, you should multiply them, and 1 x 1 = 1, which is why I thought just a picture must equal two. Then, I suppose half a picture might equal one. I’ve lost myself. I wish I’d never read this! 🙂

That’s the issue exactly. The pictures are ambiguous and mean that a specific answer cannot be provided. There is no ‘right’ answer to the question and it’s actually a particularly nasty trick (which is why I object to them) because it carries the implication that there should be one. A lot of ‘psychological’ tests fall into this category – traps and tricks that allow the test creator to feel ‘superior’ to their victim, who’s sitting the test.

Logically, how you define the first ‘picture’ is how you should define all the pictures. Thus if you are happy with [one single] apple representing the number 10 then it doesn’t make sense to move the goal posts with the bananas and coconuts. So even as an exercise in straight logic, the quibble about the ‘meaning’ of the bananas and coconuts doesn’t work.

Isn’t this how Common Core works? I agree with you Matthew, this test is too ambiguous to figure a correct answer.

I don’t know much about the Common Core except the bits I’ve seen appear to be an effort by intellectuals to present ideas in their most complex and confusing forms – it certainly isn’t the way I think.