MathDB

Math Prize 2021 Problem 4

Source:

September 19, 2021

Math Prize for Girls

Problem Statement

For a positive integer

n

, let

v(n)

denote the largest integer

j

such that

n

is divisible by

2^j

. Let

a

and

b

be chosen uniformly and independently at random from among the integers between 1 and 32, inclusive. What is the probability that

v(a) > v(b)