A few nights ago as I was drifting off to sleep I thought of the following puzzle: suppose you go out for ice cream and there are three flavours to choose from: passionfruit, coconut, and squid ink. You like all three equally, but can only choose one, and so you decide you want to make the choice randomly and with equal probability to each.

However, the only device you have to generate random numbers is a fair coin. So, how you do use your fair coin to choose between the three options of ice cream?

Of course, you can only use coin flips to make your choice. For instance, cutting the coin into three equal pieces, putting them in a bag to create a new stochastic process does not count.