Problem:
A base- three-digit number is selected at random. Which of the following is closest to the probability that the base- representation and the base- representation of are both three-digit numerals?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The largest base- three-digit number is and the smallest base- three-digit number is . There are integers that satisfy , and three-digit numbers altogether, so the probability is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions