Skip to main content

2022/23 AHSMC Part 1 Problem 3

Problem 3 of 16

The number of positive integers nn such that 5n5n has 44 digits and 4n4n has 33 digits is

Answer choices

Show solution

Solution

Since 4n4n has 33 digits then 4n<10004n < 1000 i.e., n<250n < 250. Now, since 5n5n should have 44 digits, 5n≥10005n \ge 1000, hence n≥200n \ge 200. Therefore, 5050 numbers have the requested property. The answer is (C).

University of Alberta