There are 50 doors in a hostel numbered 1 to 50. All the doors were closed at the beginning. There were 50 people numbered 1 to 50, who were playing an interesting game. Each player reverses the state of the door, if the door number is divisible by his number. For instance, the person numbered 1, would open all the doors. Then the person numbered 2, would close all the even numbered doors. The process goes on till all the 50 people have had their chance. Find the number of doors that are closed at the end of the game.

Question

There are 50 doors in a hostel numbered 1 to 50.  All the doors were closed at the beginning.  There were 50 people numbered 1 to 50, who were playing an interesting game. Each player reverses the state of the door, if the door number is divisible by his number. For instance, the person numbered 1, would open all the doors. Then the person numbered 2, would close all the even numbered doors. The process goes on till all the 50 people have had their chance.  Find the number of doors that are closed at the end of the game.

anonymous · Answer

@campbell_st @mathslover @mathstudent55  @jim_thompson5910

jim_thompson5910 · Answer

Hint: this has to do with factorization and factoring numbers

jim_thompson5910 · Answer

more specifically, it has to do with the number of factors for any given type of number

anonymous · Answer

I didn't get you

jim_thompson5910 · Answer

do a simulation on paper but do so for doors 1 through 10 (instead of 50)

which doors are closed at the end of the game?

anonymous · Answer

okay than

anonymous · Answer

The answer will be 40. As per the above mentioned details.

anonymous · Answer

Thanks! I am now in hurry!

jim_thompson5910 · Answer

the answer isn't 40