[Eikou]

This is not a good way to phrase this riddle. First of all, you're taking the abstract concept of infinity and applying it to the concrete example of quarters on a table. That doesn't make any sense, so of course you're going to lead to confusion like diamond's (who did present a valid point). Instead, pick an arbitrary large number. Here's an easier-to-use version of the riddle:

Frozen Fingers Problem:

You are lost on the Arctic Tundra. And, unfortunately, you have been stricken blind. You meet a stranger who says he will help you find your way home if you can solve this problem. There are 100 quarters lined up on the frozen ground. Twenty of those quarters are "heads" up. The rest are "tails" up. You have to figure out how to make 2 groups of quarters that both have the same number of up turned "heads". But remember you cannot see the quarters because you are blind. And you cannot feel the quarters because your fingers are frozen.

There are still some logical issues with this one though. For example, if you're blind and numb, how do you pick up the quarters to begin with. Still, it's a little easier to wrap your head around. The answer that the riddle is looking for (barring balancing them sideways or anything like that) is a certain flipping pattern that I won't describe in case someone else wants to solve it.