Answer to December 3, 2001 Problem

The Factorial Problem

For all positive integers n, the symbol n! denotes the product of the first n positive integers. In other words, 4! = 4x3x2x1 = 24.

Find the value of n for which
(3!)(5!)(7!) = n!

Solution: The answer is 10.
Notice that (3!)(5!) = (6)(120) = 720 = 8*9*10.
then, (7!)(3!)(5!) = (7!)(8*9*10) = 10!
and n = 10.


Correctly solved by:

1. Keith Mealy Cincinnati, Ohio
2. Rick Jones Kennett Square, Pennsylvania
3. Sean Giddings Shawnee Mission, Kansas
4. Carter Wallace Columbus, Georgia
5. Richard K. Johnson La Jolla, California
6. David and Judy Dixon Bennettsville, South Carolina
7. Walt Arrison Philadelphia, Pennsylvania
8. Chip Schweikarth Winchester, Virginia
9. John Beasley Winchester, Virginia
10. Travis Riggs Winchester, Virginia
11. David Powell Winchester, Virginia
12. Nick von Keller Winchester, Virginia
13. John Funk Ventura, California
14. Bob Hearn Winchester, Virginia
15. Izzy Kushner Closter, New Jersey
16. Janine Oliver Winchester, Virginia
17. Matt Crandell Winchester, Virginia
18. George Gaither Winchester, Virginia
19. Laurence O'Neill Winchester, Virginia
20. Jaime Garcia Winchester, Virginia
21. Renata Sommerville Austin, Texas
22. Geoff Keith Santa Monica, California
23. Justin Collins Winchester, Virginia
24. Carter Staples Columbus, Georgia
25. Matt McMurtry Arlington, Virginia
26. Stevenson Gravlee Columbus, Georgia
27. Jeffrey Ward Columbus, Georgia
28. John Lybarger Calhoun Community College, Alabama
29. Wilds Ogie Columbus, Georgia
30. Ghazaleh Joukar Winchester, Virginia
31. Ellen Sankovich Winchester, Virginia
32. Ashley Maignan Columbus, Georgia
33. James Alarie University of Michigan -- Flint
34. Katrina Lenexa, Kansas
35. Josh Reifsnyder Winchester, Virginia
36. Jeffrey Bentz Shawnee Mission, Kansas