November 26, 2001
Problem of the Month

Combination Lock Problem

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 the 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

Send any comments or questions to: David Pleacher