Binary Coins

Last summer I had the opportunity to meet a number of talented computer science teachers at a 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 teaching the concept. Students are only given one of each coin and 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 to use with my own students. Although, I used them slightly differently. In my scenario they were tokens for a new transit system going in. Just like on a city bus riders 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 is, "What combination of tokens you would need to guarantee you could take any ride?" I printed three or four sets and mixed them together for my students. Depending on your clas