Tricky 1,for smart people only!!!!?

Question

An office block contains a very long corridor, containing 100 doors in a row, numbered from 1 to 100 inclusive. By a very odd coincidence, there are also 100 people working along this corridor. One day, one of these people comes into the corridor and closes all of the doors. After this person has left, a second person enters the corridor and, starting with door 2, opens every second door.

After this is completed, a third person comes along and, starting at door 3, checks every third door, opening it if it is closed, and closing it if it is open. After this, a fourth person comes along, and checks every fourth door, opening it if it is closed and closing it if it is open. This continues for the 5th, 6th, 7th person and so on until the 100th person comes and checks the 100th door, opening it if it is closed and closing it if it is open. (The 5th person checks every 5th door, the 6th person checks every 6th door and so on.)

After the 100th person has come and left, how many of the 100 doors on the corridor are closed?

NOTE: The 3rd person will check doors number 3, 6, 9, ... up to door 99 and then leave. Similarly, the 7th person checks doors 7, 14, 21, ... up to door 98 and then leaves and so on.

Answer 1

10

It's the number of square numbers up to 100.

Why? Because it has an odd number of factors. Therefore the doors will be closed. Those with an even number of factors will be open (pairs of closed,open)

Answer 2

1

Answer 3

All numbers which have an even number of factors are open. So, the closed doors are numbers with odd factors.

the only type of numbers with odd factors are squares. since there are 10 square between 1 to 100 inclusive, the number of closed doors are 10.

Answer 4

1 door left closed cause the first person closed all the doors then all the others started opening at number , then 3 and so on. So the very first door is the only one left closed.

I think thats right, not to sure.... mmmm the grey matter is a bit rusty on a Monday?!

Answer 5

100

Answer 6

Stop thinking, just open the closed doors,
then welcome to the 100th . . .
then close for the day, and a good morning
for tomorrow.

Answer 7

the first door is the only one open.

Answer 8

all the doors are closed.

Answer 9

Dear smart dawg***


TEN !!!!


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peppa-ann