MathDB

N4

Part of 2022 Balkan MO Shortlist

Problems(1)

Interesting NT

Source: BMO Shortlist 2022, N4

5/13/2023
A hare and a tortoise run in the same direction, at constant but different speeds, around the base of a tall square tower. They start together at the same vertex, and the run ends when both return to the initial vertex simultaneously for the first time. Suppose the hare runs with speed 1, and the tortoise with speed less than 1. For what rational numbers qq{} is it true that, if the tortoise runs with speed qq{}, the fraction of the entire run for which the tortoise can see the hare is also qq{}?
number theory