1975 AHSME Problems/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
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