The championship of Super Arcade, a two player game, is decided by the following rules:
To be champion, a player must win 2 consecutive games; or
if each player wins 3 games, the winner of the 7th game is champion.
The scorekeeper must keep track of who wins each game, and in what order.
How many different outcomes can she record?
In other words, if there are two players, in how many different ways can one of them be champion (for example, player one winning the first two games is one outcome; player two winning the first, third and fourth games is another).
Solution to Problem:
The answer is 14 different outcomes.
Letting F represent the first player and S represent
the second player, all fourteen different outcomes are listed below:
| 1st Game | 2nd Game | 3rd Game | 4th Game | 5th Game | 6th Game | 7th Game |
| F | F | |||||
| F | S | S | ||||
| F | S | F | F | |||
| F | S | F | S | S | ||
| F | S | F | S | F | F | |
| F | S | F | S | F | S | F |
| F | S | F | S | F | S | S |
| S | S | |||||
| S | F | F | ||||
| S | F | S | S | |||
| S | F | S | F | F | ||
| S | F | S | F | S | S | |
| S | F | S | F | S | F | F |
| S | F | S | F | S | F | S |
Correctly solved by:
| 1. Richard K. Johnson | La Jolla, California |
| 2. Keith Mealy | Cincinnati, Ohio |
| 3. Ricki Stern | Highland Park, New Jersey |
| 4. Rick Jones | Kennett Square, Pennsylvania |
| 5. Walt Arrison | Philadelphia, Pennsylvania |
| 6. Joe Heintz | Manchester, Tennessee |
| 7. Renata Sommerville | Austin, Texas |
| 8. Gusti Oggenfuss | Montet, Switzerland |
| 9. Kirstine Wynn | Winchester, Virginia |
| 10. David and Judy Dixon | Bennettsville, South Carolina |