Difference between revisions of "1992 AIME Problems/Problem 15"
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Revision as of 19:24, 4 July 2013
Problem
Define a positive integer to be a factorial tail if there is some positive integer
such that the decimal representation of
ends with exactly
zeroes. How many positive integers less than
are not factorial tails?
Solution
The number of zeros at the end of is
.
Note that if is a multiple of
,
.
Since , a value of
such that
is greater than
. Testing values greater than this yields
.
There are distinct positive integers,
, less than
. Thus, there are
positive integers less than
that are not factorial tails.
See also
1992 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Last Question | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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