2003 AIME I Problems/Problem 1
Problem
Given that
where 
and 
are positive integers and is as large as possible, find 
Solution
Note that![\[{{\left((3!)!\right)!}\over{3!}}= {{(6!)!}\over{6}}={{720!}\over6}={{720\cdot719!}\over6}=120\cdot719!.\]](http://latex.artofproblemsolving.com/8/6/8/868eddc32a5e4c6b77ab9b1510ff91597ff430c9.png)
Because 
, we can conclude that 
. Thus, the maximum value of is 
. The requested value of 
is therefore 
.
~yofro
See also
| 2003 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
