# Solution : Free cab ride

Standard

It has been one month since I posted the puzzle. But since nobody solved it, here is my solution.

Let’s consider examples:

 Number of people Number of free rides 1 0 2 2 3 4 4 6

I can illustrate above counting with simple figure:

Each line segment represent two free rides for the group, since every time you refer someone, both referee and new customer get free ride.

From above observations we can conclude by Principle of Mathematical Induction, (try yourself!):

A group of $n$ people can enjoy at most $2(n-1)$ rides.