I found a similar problem and solution, no longer need a solution to this.
I'm unsure how to tag this problem, so it may or may not need to be moved.
Given n coins, what is the least number of groups you can divide the coins in to such that you can reach any whole number from 1 to n by adding any number of groups together.
It's been a while since I've messed with a problem like this. My first thought was just count how many times you can do n/2 until you get to 1, but suppose n is prime, or odd, what would result?