Clock jumping 34 or 47 seconds will become a perfect square
Source: Iran MO second round 2024 P1
April 18, 2024
number theorycombinatorics
Problem Statement
Kimia has a weird clock; the clock's second hand moves 34 or 47 seconds forward instead of each regular second, at random. As an example, if the clock displays the time as , the following times could be displayed in this order:
Prove that the clock's second hand would eventually land on a perfect square.