Another kind of problem with numbers

That first number problem needed some simple logic to figure out. The trick was that you had to go beyond the basic logic that you thought you knew. The second one used more of a problem-solving type of logic, because you need to figure out why you can't shave off enough time and then solve it accordingly. I know a lot of different ones, but a lot of them use the same type of thinking as the first two, so it would be somewhat redundant. If anyone is able to get the answer to that second one, email me and I will post your name.
I have two more old-time word problems in mind right now. One is easy, but the other one is like stupid-hard. They each use different kinds of thinking, but to me they seem to all be related.
Anyway, I'm working on the drafts for them to put up here.

Here is the first one, it uses what I would call "systematic thinking":

Suppose you had a dollar.
Now suppose you had someone make change for it.
They could give you a silver dollar. That would be one coin.
They could give you two half-dollars. Two coins.
They could give you a half-dollar and two quarters. Three coins.
Question: what is the smallest number of coins that could not add to exactly one dollar?

See, not hard. Just stubborn. Good luck.