How can $3$ friends pay $5$ cents each to enter some place, when they only have coins of $10$, $15$ and $20$ cents (unlimited of them)?
I started by noticing that each of them must pay an odd quantity and only giving a coin of $15$ to another person changes the parity of both people(the one who gives and the one who receives. So if every one starts at paying an even quantity ($0$), some changes must be done to ensure every one of them has payed an odd quantity and then paying with coins of $10$ or $20$ until you have payed all of it, but this is imposible as you cannot go from $000_2$ to $111_2$ changing two digits at a time.
So here is the problem, my conclusion is that this is not possible, but the problem is in a book of problems, which the logical thing is that it has a valid answer.