IBM Ponder This #158 · June 2011

The winner of the IBM Global Entrepreneur of the Year contest for 2010 was Streetline (see here details and a great six-minute pitch on their innovative parking system), so we decided to focus this month's challenge on parking.

This challenge is based on a puzzle we heard from Yaniv Shmueli, who heard it himself a few years ago.

Let's assume that cars have a length of two units and that they are parked along the circumference of a circle whose length is 100 units, which is marked as 100 segments, each one exactly one unit long.

A car can park on any two adjacent free segments (i.e., it does not need any extra maneuvering space).

Our question is as follows: Let's assume that we start with an empty circle. We add one car at a time, and each car parks in a random free space (aligned to a unit length), till no such place exists. What is the expected number of cars that can park along that 100-unit-long circle?

Solution

Best opened after a real attempt

To be added.