Question

In a jail with 100 rooms, all locked initially, 100 rioters
break in and disturb the rooms in the following way. First
one stops at all rooms and opens them all. Second rioters
stops at rooms numbered 2, 4, 6, . . . and locks open rooms,
and leaving the other rooms as they were. The third rioter stops at rooms numbered 3, 6, 9, . . . and again opens a
locked room and locks an open room, leaving others undisturbed. And this process continues. After all the 100 rioters
have left which rooms would be open?

Answer 1

i dont know! :P
any good reasons ?

Answer 2

the ones that will be open are the squares (i.e. 4, 9, 16, 25, etc)

Answer 3

the ones that will be closed are the not squares

Answer 4

@lgbasallote I think room 1 will be surely opened..

Answer 5

yes it will

Answer 6

1 is a perfect square isnt it

Answer 7

1 opens 4
2 closes 4
4 opens 4

Answer 8

100 th room

Answer 9

for 9

1 opens 9
3 closes 9
9 opens 9

Answer 10

for 16

1 opens 16
2 closes 16
4 opens 16
8 closes 16
16 opens 16

Answer 11

for 25

1 opens 25
5 closes 25
25 opens 25

Answer 12

for 36

1 opens 36
3 closes 36
6 opens 36
12 closes 36
36 opens 36

Answer 13

for 49

1 opens 49
7 closes 49
49 opens 49

Answer 14

I guess the number which has odd number of factors will be open

Answer 15

in 36 you missed some in between but result remains open,,hmm
i see maybe you're correct..

Answer 16

And the room number which has even number of factors will be closed

Answer 17

for 64

1 opens 64
2 closes 64
4 opens 64
8 closes 64
16 opens 64
32 closes 64
64 opens 64

Answer 18

what comesafter 64 again?

Answer 19

81

1o
3c
9o
27c
81o

Answer 20

yes that

Answer 21

finally 100

1o
2c
4o
5c
10o
20c
25o
50c
100o
nice..
thanks..

Answer 22

welcome

Answer 23

can there be some reason why its always sq. no ?
or its just a pattern ? ! ?

Answer 24

it's a tedious proof... lol

Answer 25

i just know the trial and error proof of it

Answer 26

I guess only sq. no have odd number of factors

Answer 27

aha..yes it seems so..lol..might make up another good ques that only sq no. have odd no. of factors! :D

Answer 28

damn i closed the quess,,wait i shall tag,,

Answer 29

@mukushla
@eliassaab

Answer 30

Oh..... got it....... I think I can prove it

Answer 31

IF its not an sq. number.... for example 12
then the factors are 1,2,3,4,6,12

Answer 32

right?

Answer 33

yes..

Answer 34

Now,