2006 AIME A Problems/Problem 4
Problem
Let be the number of consecutive 0's at the right end of the decimal representation of the product
Find the remainder when
is divided by 1000.
Solution
Clearly, . Now, consider selecting
of the remaining
values. Sort these values in descending order, and sort the other
values in ascending order. Now, let the
selected values be
through
, and let the remaining
be
through
. It is now clear that there is a bijection between the number of ways to select
values from
and ordered 12-tuples
. Thus, there will be
such ordered 12-tuples.
See also
2006 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |