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i dont know! :P
any good reasons ?

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

the ones that will be closed are the not squares

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

yes it will

1 is a perfect square isnt it

1 opens 4
2 closes 4
4 opens 4

100 th room

for 9
1 opens 9
3 closes 9
9 opens 9

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

for 25
1 opens 25
5 closes 25
25 opens 25

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

for 49
1 opens 49
7 closes 49
49 opens 49

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

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

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

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

what comesafter 64 again?

81
1o
3c
9o
27c
81o

yes that

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

welcome

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

it's a tedious proof... lol

i just know the trial and error proof of it

I guess only sq. no have odd number of factors

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

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

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

right?

yes..

|dw:1345558048314:dw|Now,

Now, lets look a sq. number ... for example 25
its factors are 1,5,5,25|dw:1345558167578:dw|

TO make it more clear......|dw:1345558421778:dw|

and sum of even numbers is always a even number

cool..i get it! nice.. :)

now lets return to my ques,,why only sq. nos should be there?

To...... write and make other understand is a very difficult......

without speaking

Am i right?

lol..you did a pretty good job sir.,thanks..

I mean it is easy for u guys........... but for others its really hard

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