shubhamsrg
  • 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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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shubhamsrg
  • shubhamsrg
i dont know! :P any good reasons ?
lgbasallote
  • lgbasallote
the ones that will be open are the squares (i.e. 4, 9, 16, 25, etc)
lgbasallote
  • lgbasallote
the ones that will be closed are the not squares

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More answers

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

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