I was in Bristol last week, where people were discussing the following problem over drinks and dinner following my talk. I hope they don’t mind my publicising a nice problem. I will tell you nothing about the solution, but I am sure you will have fun thinking about it. It has a nice variation on the usual problem of this type.
Two people (Alice and Bob, of course) share a circular pizza. A positive integer n is given. Alice cuts the pizza into n slices with radial cuts from the centre. Then Bob chooses a slice. The players take turns in choosing slices, but the chosen slice must be contiguous with those already taken.
How much does each player get if both play optimally (assuming they both want to maximise their share)?