Modifying the locker problem

Level pending

A boy enters school to see 5100 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 ! 2! , then, he closes all lockers that are multiples of 3 ! 3! , however, if the locker is already closed, he opens it. He repeats this for 4 ! 4! , 5 ! 5! , 6 ! 6! and lastly 7 ! 7! . How many lockers would still be open?

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


The answer is 3224.

Charlton Teo by Charlton Teo , 21, Singapore

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1 solution

Brock Brown
Jan 5, 2015 
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from math import factorial
lockers = 5100
closed = set()
# for each possible step length
for i in xrange(2,8):
    # go back to the first locker
    position = 1
    # set new step length
    step = factorial(i)
    # walk by lockers
    while position <= lockers:
        # if it's open
        if position not in closed:
            # close the locker
            closed.add(position)
        # if it's closed
        else:
            # open the locker
            closed.remove(position)
        # go to next locker
        position += step
print "Answer:", lockers - len(closed)

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