Question 90
Kimia has a strange clock. Its minute hand doesn't work correctly. At any moment, instead of moving one second, it randomly jumps $34$ or $47$ seconds. For example, if at one moment the clock shows $12{:}23{:}05$, in the next moments it might show
$12{:}23{:}39$, $12{:}24{:}13$, $12{:}25{:}00$, $12{:}25{:}34$, $12{:}26{:}21$, ...
Prove that there is always a moment that the second hand shows a perfect square.
$12{:}23{:}39$, $12{:}24{:}13$, $12{:}25{:}00$, $12{:}25{:}34$, $12{:}26{:}21$, ...
Prove that there is always a moment that the second hand shows a perfect square.