shubhamsrg
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?
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shubhamsrg
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i dont know! :P
any good reasons ?
lgbasallote
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the ones that will be open are the squares (i.e. 4, 9, 16, 25, etc)
lgbasallote
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the ones that will be closed are the not squares
sauravshakya
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@lgbasallote I think room 1 will be surely opened..
lgbasallote
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yes it will
lgbasallote
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1 is a perfect square isnt it
lgbasallote
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1 opens 4
2 closes 4
4 opens 4
Yahoo!
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100 th room
lgbasallote
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2
for 9
1 opens 9
3 closes 9
9 opens 9
lgbasallote
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2
for 16
1 opens 16
2 closes 16
4 opens 16
8 closes 16
16 opens 16
lgbasallote
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2
for 25
1 opens 25
5 closes 25
25 opens 25
lgbasallote
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2
for 36
1 opens 36
3 closes 36
6 opens 36
12 closes 36
36 opens 36
lgbasallote
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2
for 49
1 opens 49
7 closes 49
49 opens 49
sauravshakya
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I guess the number which has odd number of factors will be open
shubhamsrg
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in 36 you missed some in between but result remains open,,hmm
i see maybe you're correct..
sauravshakya
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And the room number which has even number of factors will be closed
lgbasallote
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for 64
1 opens 64
2 closes 64
4 opens 64
8 closes 64
16 opens 64
32 closes 64
64 opens 64
lgbasallote
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what comesafter 64 again?
shubhamsrg
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81
1o
3c
9o
27c
81o
lgbasallote
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yes that
shubhamsrg
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finally 100
1o
2c
4o
5c
10o
20c
25o
50c
100o
nice..
thanks..
lgbasallote
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welcome
shubhamsrg
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can there be some reason why its always sq. no ?
or its just a pattern ? ! ?
lgbasallote
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it's a tedious proof... lol
lgbasallote
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i just know the trial and error proof of it
sauravshakya
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I guess only sq. no have odd number of factors
shubhamsrg
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aha..yes it seems so..lol..might make up another good ques that only sq no. have odd no. of factors! :D
shubhamsrg
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damn i closed the quess,,wait i shall tag,,
shubhamsrg
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@mukushla
@eliassaab
sauravshakya
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Oh..... got it....... I think I can prove it
sauravshakya
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IF its not an sq. number.... for example 12
then the factors are 1,2,3,4,6,12
sauravshakya
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right?
shubhamsrg
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yes..
sauravshakya
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|dw:1345558048314:dw|Now,
sauravshakya
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Now, lets look a sq. number ... for example 25
its factors are 1,5,5,25|dw:1345558167578:dw|
shubhamsrg
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hmm..so every no. will have even no. of factors if we count same no. twice..really ? that quite amazing!
sauravshakya
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If it is not a sq. number than there will always be a unique number for its factor.... so that their product will be that number
sauravshakya
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TO make it more clear......|dw:1345558421778:dw|
sauravshakya
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and sum of even numbers is always a even number
shubhamsrg
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cool..i get it! nice.. :)
shubhamsrg
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now lets return to my ques,,why only sq. nos should be there?
sauravshakya
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To...... write and make other understand is a very difficult......
sauravshakya
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without speaking
sauravshakya
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Am i right?
shubhamsrg
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lol..you did a pretty good job sir.,thanks..
sauravshakya
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I mean it is easy for u guys........... but for others its really hard
shubhamsrg
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am not very good at the subject sir,,so explaining to me always takes some effort! see,,am a bad student! hmm..
nevermind,,back to the ques please!
why only sq. nos should be there?
mukushla
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