A standard combination lock has 40 numbers (0 - 39).
Suppose the lock is positioned as in the diagram below,
with the dial pointing to 0.
Use the standard coordinate system where the origin is
at the center of the lock and the positive x-axis extends
from the origin through the number 0 on the lock. Positive
angles are measured in a counter clockwise rotation.
To open the lock, you must first move the dial -135 degrees. Then move the dial +378 degrees. Then move the dial -99 degrees.
Translate that into a combination explaining whether to move the dial right or left and telling what number to stop at. Don't forget that the numbers of the combination are the ones which appear at the indicator.
Solution to Problem:
The combination is:
Turn the dial RIGHT stopping at 25.
Turn the dial left going past 25 and then stopping at 27.
Turn the dial RIGHT stopping at 16.
Since there are 40 numbers on the combination lock and there are
360 degrees in a circle, the arc between any two consecutive numbers
represents 9 degrees. Turning the dial -135 degrees means moving to
the right 15 numbers (which means 25 will be at the indicator).
Then going +378 degrees means moving 42 numbers to the left (which
will stop at 27). Then -99 degrees moves RIGHT 11 numbers, stopping
at 16.
Correctly solved by:
| 1. Richard K. Johnson | La Jolla, California |
| 2. Walt Arrison | Philadelphia, Pennsylvania |
| 3. Tony Wu | Fort Collins, Colorado |
| 4. Keith Mealy | Cincinnati, Ohio |
| 5. John Lybarger | Calhoun Community College, Alabama |
| 6. Izzy Kushner | Closter, New Jersey |
| 7. David Powell | Winchester, Virginia |
| 8. David and Judy Dixon | Bennettsville, South Carolina |
| 9. Bob Hearn | Winchester, Virginia |
| 10. Adam Banning | Lenexa, Kansas |
| 11. John Beasley | Winchester, Virginia |
| 12. Sean Giddings | Shawnee Mission, Kansas |
| 13. John Funk | Ventura, California |
| 14. Travis Riggs | Winchester, Virginia |
| 15. Nick Katz | Shawnee Mission, Kansas |
| 16. Jaime Garcia | Winchester, Virginia |
| 17. Renata Sommerville | Austin, Texas |
| 18. Matt McMurtry | Arlington, Virginia |