So this image has been floating around the big truck:

“If you choose an answer to this question at random, what is the chance you will be correct?

a) 25%

b) 50%

c) 60%

d) 25%”

It’s meant to be a gotcha, based on the reader’s (presumed) assumption that choosing an answer at random means each of the four answers is equally likely to be chosen. That gives a 1 in 4 chance of getting the “right” answer — but both a) and d) correspond to that probability, which means that there’s a 2 in 4 chance of getting an answer of 25%… which corresponds to the answer in b), but there’s only a 1 in 4 chance that you’ll select b). There’s no steady-state solution to this iterative process, so most people will mull it over and conclude “brain go splodey”, while a few math and comp-sci nerds will recognize a self-referential system and jump immediately to Russell and Gödel.

There is, of course, a satisfyingly smart-assed approach, which relies upon the fact that random numbers are chosen from some sort of *distribution*. This remains unspecified in the question. If we stipulate that random answers are distributed such that either b) is chosen 50% of the time or c) is chosen 60% of the time, we can make either one of those the correct answer.

Stupid math tricks: always fun on the internet.

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Isn’t it just all-Cretans-are-liars, obfuscated enough that it’s not immediately obvious? NTTAWWT, obv.

Assuming a uniform distribution of random answers, yeah, it’s the same kind of paradox: you alternate between two incompatible truth assignments, each of which implies the other.

Another smart-ass response that I came up with:

0%

Another smart-ass response would be that they are asking a

humanto choose a random value, not a computer. Humans are pretty bad at choosing random numbers; I’m not sure how bad they are in numeric terms, but a & d would most likely be chosen much less, and c much more. It’s not impossible that a & d would between them be chosen 25% of the time, or c would be chosen 60% of the time.Which gets back to the “didn’t specify a distribution” dodge (or insight).

IIRC students tend to be biased slightly towards answering c) on four-option multiple-choice questions, but I very much doubt they’re 60% biased. A quick google didn’t turn up anything I could find on the subject before I lost interest, but I lost interest pretty quickly.

When this hit, I asked, “What would be a significantly different answer from any other?”

.