Difference between revisions of "1975 AHSME Problems/Problem 18"
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Revision as of 11:52, 26 December 2020
Problem 18
A positive integer with three digits in its base ten representation is chosen at random,
with each three digit number having an equal chance of being chosen. The probability that
is an integer is
Solution
In order for to be an integer,
has to be an integer power of
. Since
is a three-digit number in decimal form,
can only be
. From
to
, there are
three-digit numbers in total.
The probability of choosing ,
, or
from
numbers is
, which gives us the answer
. ~jiang147369