I have been walking around campus before class starts and I am seeing tons of people playing video games in the common areas.  I have never really seen this before, but I always thought it would be neat to hook up a gaming console to a public TV.  But I am seeing people bring their own TVs to the public areas and play in areas like right outside of Chick-Fil-A and Dominos.   Something I would imagine would be lots of work. 

Let’s pretend we want to expand our friend circles and wanted to play with them.   For the sake of this problem, let’s assume they are always nice people, and they will let you join if you just ask.  If there are less than 4 people playing, they will let you join.  If there is more than for people, you will continue to the next group (Group sizes will be from 1 to at least 4).  You will have a 50% chance if you play with this group again after each game.  Keep going through each group until you have played 20 games.

It is ok if they play more than 20 games, as long as you don’t visit another group after you reach 20 or more. 

Sample Flowchart

1. Set amount of games played to 0
2. Set the amount of groups you have gone to to 0
3. while amount of games is less than 20 do the following:
   1. Add one to the groups visited.
   2. Print out what number group this is.
   3. If it is the first game generate a number between 1-4 and if it is less than 4, play the game.
      1. After the first play, generate a random number that you can use to determine a 50% odds.  On one half play a game again, until you generate something on the other half.