Wait What? Does this even make sense?

Logic Level pending

How many letters are there in the correct answer to this question?

The answer is 4.

1 solution

Ahmad Khamis
Feb 2, 2016

This can only be done by trial and error. Suppose you choose $1$ . One notices that "one" has three letters which does not equal $1$ . Carry on this until you get to the number $4$ . $4$ has four letters which equals $4$ . Therefore $4$ is the correct answer.

Moderator note:

You seem to be assuming that there can only be one correct answer. Please justify that assumption.

Calvin Lin Staff - 5 years, 3 months ago

I'm not assuming. This was originally a multiple choice question and now I made it an open ended question.

Ahmad Khamis - 5 years, 3 months ago

You still have to justify why there are no other possible answers.

Calvin Lin Staff - 5 years, 3 months ago

@Calvin Lin – I can't think of any way to prove it, other than by trial and error.

Ahmad Khamis - 5 years, 3 months ago

@Ahmad Khamis – Trial and error doesn't prove that no other solutions exists. It only shows that "for the finitely many values which you tried, there are no other answers".

Calvin Lin Staff - 5 years, 3 months ago

@Calvin Lin – Well then I'm not sure how to prove it.

Ahmad Khamis - 5 years, 3 months ago

@Ahmad Khamis – One possible approach is to say that

Any number from 10 to 99 will use at most (say) 40 characters.
Any number from 100 to 999 will use at most 5 + 7 + 40 characters.
Any number from 1000 to 9999 will use at most 5 + 8 + 5 + 7 + 40 characters.
So on and so forth. So, we only need to check the first few (finitely many) cases.

Calvin Lin Staff - 5 years, 3 months ago

Wait What? Does this even make sense?

The answer is 4.

1 solution

Moderator note:

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