Binary Coins

I was at workshop for CS50AP in Redmond. During the discussion on binary someone mentioned a lesson they do using coins with binary values as a way to begin. That is to say there is a 1, 2, 4, and so on. They are only given one of each coin. Students are told they will be going to a candy store and must pay in exact change. They quickly realize that no matter what the price (up to a maximum) they can always pay in exact change. I decided I needed a set. Although, I might use them slightly differently. In my scenario I might turn them into bus tokens for a new transit system going in. Like any bus they must pay in exact change and the price of a ride depends on a variety of factors, but ranges from $0.01 to $2.50. The question would be, “What is the minimum number of coins you would need to be able to make any ride?” I’d print three or four sets and mix them together and give them to the students.”