# Modifying the locker problem

Level pending

A boy enters school to see $$5100$$ lockers opened. He was tasked by his teacher to close all of the lockers. Being a very bored person, he decides to close them in a peculiar manner. First, he closes all lockers that are multiples of $$2!$$, then, he closes all lockers that are multiples of $$3!$$, however, if the locker is already closed, he opens it. He repeats this for $$4!$$, $$5!$$, $$6!$$ and lastly $$7!$$. How many lockers would still be open?

My apologies, I posted this question previously with the wrong answer

×