Sharing pizza

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)?

Advertisements

About Peter Cameron

I count all the things that need to be counted.
This entry was posted in mathematics and tagged , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s