$$100$$ boys are standing in front of their lockers, numbered from $$1$$ to $$100$$. ~At the beginning, ~all lockers are unlocked. ~$$A$$ teacher calls out \textquotesingle$$3$$\textquotesingle, only those boys whose locker numbers are divisible by $$3$$ will lock their lockers. ~The teacher then calls out \textquotesingle$$5$$\textquotesingle, only those boys whose locker numbers are divisible by $$5$$ will unlock their lockers if they are locked, ~or lock their lockers if they are unlocked. ~How many lockers will be unlocked at the end? 
Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Questions involving Square Numbers