Answer to the Problem of the Week
for the week of February 27, 2006

The Judge Problem

On July 1, 2002 Paul Martinek, publisher of Lawyers Weekly USA, was a guest on the national television news and interview show The O'Reilly Factor.   The topic was the ruling by the Ninth Circuit Court in California.   The court held that requiring sudents in public schools to recite the Pledge of Allegiance is unconstitutional because it contains the phrase "under God."

The panel that issued the ruling consisted of three judges, chosen at random from the larger number in the Ninth Circuit.   Martinek commented, "Because there are 45 judges in the Ninth Circuit, there are 3,000 different combinations of three-judge panels."

Mr. Martinek's math is a little rusty.   Help him out by answering the following questions:
(1) If a three-judge panel is to be chosen from a pool of forty-five judges, how many different panels are possible?
(2) How many judges would have to be in the Ninth Circuit for the statement that "there are 3,000 different combinations of three-judge panels" to be correct?


 

Solution to the Problem:

The answers are (1) 14,190 and (2) 27 or 28.



Correctly solved by:

1. Jim Arrison Norristown, Pennsylvania
2. Kunal Singh Kendriya Vidyalaya School
Happy Valley, Shillong, India
3. Sagar Patel Brookstone School
Columbus, Georgia
4. Magdy Essafty Alexandria , Egypt
5. Emily Powell John Handley High School
Winchester, Virginia
6. Tristan Collins Virginia Tech
Blacksburg, Virginia
7. Azusa Inaba John Handley High School
Winchester, Virginia
8. James Alarie University of Michigan -- Flint
Flint, Michigan
9. David & Judy Dixon Bennettsville, South Carolina
10. Yassee Pirooz Harrisonburg High School
Harrisonburg, Virginia
11. Karl Jaeger Mountain View High School
Mountain View, Wyoming
12. Kshitij (Chris) Mehrotra Elgin, Illinois
13. GK Bridgewater, NJ
14. Larry Schwartz Norwalk, Connecticut
15. Laura Minnis Harrisonburg High School
Harrisonburg, Virginia
16. Ben Reedy ----------
17. Laura Gronauer ----------
18. Jack Kang Chelmsford High School
Chelmsford, Massachusetts
19. Jess Thorpe Brookstone School
Columbus, Georgia
20. Julianne Harris John Handley High School
Winchester, Virginia
21. Andrew Montoya John Handley High School
Winchester, Virginia
22. Carolyn Shuler Brookstone School
Columbus, Georgia
23. Patrick Rose North Posey Sr High School
Poseyville, Indiana
24. Javier Johnson ----------
25. Ben Bassett Sewell, New Jersey
25. Leonard Sugar ----------