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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?
 one year ago
 one year ago
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?
 one year ago
 one year ago

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shubhamsrgBest ResponseYou've already chosen the best response.1
i dont know! :P any good reasons ?
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.2
the ones that will be open are the squares (i.e. 4, 9, 16, 25, etc)
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.2
the ones that will be closed are the not squares
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.2
@lgbasallote I think room 1 will be surely opened..
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.2
1 is a perfect square isnt it
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.2
1 opens 4 2 closes 4 4 opens 4
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.2
for 9 1 opens 9 3 closes 9 9 opens 9
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.2
for 16 1 opens 16 2 closes 16 4 opens 16 8 closes 16 16 opens 16
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.2
for 25 1 opens 25 5 closes 25 25 opens 25
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.2
for 36 1 opens 36 3 closes 36 6 opens 36 12 closes 36 36 opens 36
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.2
for 49 1 opens 49 7 closes 49 49 opens 49
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.2
I guess the number which has odd number of factors will be open
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.1
in 36 you missed some in between but result remains open,,hmm i see maybe you're correct..
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.2
And the room number which has even number of factors will be closed
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.2
for 64 1 opens 64 2 closes 64 4 opens 64 8 closes 64 16 opens 64 32 closes 64 64 opens 64
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.2
what comesafter 64 again?
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.1
81 1o 3c 9o 27c 81o
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.1
finally 100 1o 2c 4o 5c 10o 20c 25o 50c 100o nice.. thanks..
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.1
can there be some reason why its always sq. no ? or its just a pattern ? ! ?
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.2
it's a tedious proof... lol
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.2
i just know the trial and error proof of it
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.2
I guess only sq. no have odd number of factors
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.1
aha..yes it seems so..lol..might make up another good ques that only sq no. have odd no. of factors! :D
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.1
damn i closed the quess,,wait i shall tag,,
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.1
@mukushla @eliassaab
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.2
Oh..... got it....... I think I can prove it
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.2
IF its not an sq. number.... for example 12 then the factors are 1,2,3,4,6,12
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.2
dw:1345558048314:dwNow,
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.2
Now, lets look a sq. number ... for example 25 its factors are 1,5,5,25dw:1345558167578:dw
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.1
hmm..so every no. will have even no. of factors if we count same no. twice..really ? that quite amazing!
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.2
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
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.2
TO make it more clear......dw:1345558421778:dw
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.2
and sum of even numbers is always a even number
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.1
cool..i get it! nice.. :)
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.1
now lets return to my ques,,why only sq. nos should be there?
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.2
To...... write and make other understand is a very difficult......
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.1
lol..you did a pretty good job sir.,thanks..
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.2
I mean it is easy for u guys........... but for others its really hard
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.1
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?
 one year ago
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