# Easy Math Puzzle – Or is it?

November 1, 2011 14 Comments

How good are you at basic math? Can you solve this simple logic puzzle? Here, give it a go and let me know how long it took you to answer:

Got it yet?

It looks easier than it is. The options are presented beautifully to cause maximum mental confusion.

As my dad put it, the answer depends on the answer. If the answer is 60%, it’s 25%. If the answer is 25% it’s 50%. If the answer is 50% it’s 25%. There’s an endless loop with no correct answer.

Don’t lose sleep, I “found” an answer, it was hidden: [edited for clarity]

Yes, I photoshopped this. I’m either cheating or engaging in outside-the-box thinking. Sometimes it’s tough to tell the difference.

My preferred set of answers would be:

- A) 25%
- B) 50%
- C) 75%
- D) 50%

Though I’m tempted to throw a “0%” in for good measure…

(Puzzle via PostSecret by way of Spencer of Ask a Mathematician/Ask a Physicist)

[Edited for clarity]

Assuming that one of the answers has to be correct (and given both the format and the context any other assumption by the author would be dishonest), the solution is incorrect.

Please try your puzzle again and see if you can come up with the right answer. Hint: there are only three possibilities.

Ike: What is your justification for the assumption that one of the answers has to be correct? (Hint: your assumption is wrong.)

This is a multiple choice format. So one of the answers has to be correct (as I said, it is dishonest not to include a choice along the lines of none of the above if none of the answers are indeed correct.)

This is a problem of conventions in the English-speaking world, so I’m guessing that this is not your first language. I think I should also point out that your last sentence is considered extremely rude by the usual standards, though that might not be the case in your country.

Now that this is cleared up, there is an unambiguous answer to the problem.

If you pick choice C at random 60% of the time and choice D at random 40% of the time, then the answer is — please wait while I generate a random value — C!

Good point! The blackboard never said the random choice had to be evenly distributed between the options listed…

The answer is 0%, but only if you *do not* include 0% as an available option.

Right, as soon as you include 0% as an option then there’s a chance people will guess it randomly (assuming there’s a non-0 chance of getting it randomly.)

Questions containing phrases like “this question” or those that refer to the correctness of the as-yet unprovided answer are trouble, and should always be answered “Yes”.

It depends on the number of options . :)

For four options it’s 25%

For five options it’s 20%

For three options it’s 33%

and so on .

Basically it’s

100%/n

where n is the number of options .

Chance is independant of accuracy or the result itself .So the answer to a chance is fixed . :D

That does not make sense, because what answer I chose decides logically whether or not my “random answer” is correct. Then the validity of my “random answer” is not random so essentially my answer is not random since the attribute which differentiates my “random answer” from other random answers is a function of my choosing.

Is the intent that the question should be understood as if it read:

“Given a 4 answer multiple choice question in which one of the answers is correct what would the chance of a random choice being the correct answer.”

As it is written I can not see that the question has any meaning.

The answer is without doubt 25%. As two of the four options says “25%” there is a 50% chance getting it right. However, this is precisely option B which is chosen at random at the desired 25% of all cases. QED.

The answer does indeed depend on ‘answer’.

Is ‘answer’ picking a, b, c or d? Or is it picking the ‘content’ of those slots? In which case the two 25%s become significant, and there are only three possible answers.

Noting that the question does _not_ read, ‘…at random from the answers below,” I choose E) 100%…