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 2 years 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?
 2 years 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?

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shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.1i dont know! :P any good reasons ?

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

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2the ones that will be closed are the not squares

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.2@lgbasallote I think room 1 will be surely opened..

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.21 is a perfect square isnt it

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.21 opens 4 2 closes 4 4 opens 4

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2for 9 1 opens 9 3 closes 9 9 opens 9

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2for 16 1 opens 16 2 closes 16 4 opens 16 8 closes 16 16 opens 16

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2for 25 1 opens 25 5 closes 25 25 opens 25

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2for 36 1 opens 36 3 closes 36 6 opens 36 12 closes 36 36 opens 36

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2for 49 1 opens 49 7 closes 49 49 opens 49

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.2I guess the number which has odd number of factors will be open

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

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.2And the room number which has even number of factors will be closed

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2for 64 1 opens 64 2 closes 64 4 opens 64 8 closes 64 16 opens 64 32 closes 64 64 opens 64

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2what comesafter 64 again?

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

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.1can there be some reason why its always sq. no ? or its just a pattern ? ! ?

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2it's a tedious proof... lol

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2i just know the trial and error proof of it

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.2I guess only sq. no have odd number of factors

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

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.1damn i closed the quess,,wait i shall tag,,

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.1@mukushla @eliassaab

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.2Oh..... got it....... I think I can prove it

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

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1345558048314:dwNow,

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

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

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.2If 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
 2 years ago
Best ResponseYou've already chosen the best response.2TO make it more clear......dw:1345558421778:dw

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.2and sum of even numbers is always a even number

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.1cool..i get it! nice.. :)

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.1now lets return to my ques,,why only sq. nos should be there?

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.2To...... write and make other understand is a very difficult......

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.1lol..you did a pretty good job sir.,thanks..

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

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.1am 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?
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