The most difficult logic puzle/problem solving question you've come across?

Question

I'd like to see it to challenge my mind. Thanks.

Answer 1

Ok try this for logic/maths. I am going to post this as a question to see what other people come up with as an answer (don't expect an answer from me though, it was too long ago that I asked my high school teacher).

A (super)man walks from point A to point B. Lets say 100miles.

Each step he takes halves the remaining distance.

However, for each step he takes he also doubles his speed.

For his first step he travels 50miles at 2mph.

When does he cross the line?

Answer 2

Not quite the MOST, but it's tough and it's a classic:

You have 12 coins which are identical in every way, except that one of them is counterfit in its weight, but you do not know which one it is or whether it is heavier or lighter than the others. (Assume, of course, that the difference is too small to tell just by holding it).

At your disposal you have a balance scale. Using this scale 3 times (no more), you must determine:

a) which coin is the fake
b) whether it is heavier or lighter than the others

Yes, it CAN be done - good luck!