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shubhamsrg Group Title

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
  • 2 years ago

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  1. shubhamsrg Group Title
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    i dont know! :P any good reasons ?

    • 2 years ago
  2. lgbasallote Group Title
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    the ones that will be open are the squares (i.e. 4, 9, 16, 25, etc)

    • 2 years ago
  3. lgbasallote Group Title
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    the ones that will be closed are the not squares

    • 2 years ago
  4. sauravshakya Group Title
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    @lgbasallote I think room 1 will be surely opened..

    • 2 years ago
  5. lgbasallote Group Title
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    yes it will

    • 2 years ago
  6. lgbasallote Group Title
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    1 is a perfect square isnt it

    • 2 years ago
  7. lgbasallote Group Title
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    1 opens 4 2 closes 4 4 opens 4

    • 2 years ago
  8. Yahoo! Group Title
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    100 th room

    • 2 years ago
  9. lgbasallote Group Title
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    for 9 1 opens 9 3 closes 9 9 opens 9

    • 2 years ago
  10. lgbasallote Group Title
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    for 16 1 opens 16 2 closes 16 4 opens 16 8 closes 16 16 opens 16

    • 2 years ago
  11. lgbasallote Group Title
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    for 25 1 opens 25 5 closes 25 25 opens 25

    • 2 years ago
  12. lgbasallote Group Title
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    for 36 1 opens 36 3 closes 36 6 opens 36 12 closes 36 36 opens 36

    • 2 years ago
  13. lgbasallote Group Title
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    for 49 1 opens 49 7 closes 49 49 opens 49

    • 2 years ago
  14. sauravshakya Group Title
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    I guess the number which has odd number of factors will be open

    • 2 years ago
  15. shubhamsrg Group Title
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    in 36 you missed some in between but result remains open,,hmm i see maybe you're correct..

    • 2 years ago
  16. sauravshakya Group Title
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    And the room number which has even number of factors will be closed

    • 2 years ago
  17. lgbasallote Group Title
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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

    • 2 years ago
  18. lgbasallote Group Title
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    what comesafter 64 again?

    • 2 years ago
  19. shubhamsrg Group Title
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    81 1o 3c 9o 27c 81o

    • 2 years ago
  20. lgbasallote Group Title
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    yes that

    • 2 years ago
  21. shubhamsrg Group Title
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    finally 100 1o 2c 4o 5c 10o 20c 25o 50c 100o nice.. thanks..

    • 2 years ago
  22. lgbasallote Group Title
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    welcome

    • 2 years ago
  23. shubhamsrg Group Title
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    can there be some reason why its always sq. no ? or its just a pattern ? ! ?

    • 2 years ago
  24. lgbasallote Group Title
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    it's a tedious proof... lol

    • 2 years ago
  25. lgbasallote Group Title
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    i just know the trial and error proof of it

    • 2 years ago
  26. sauravshakya Group Title
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    I guess only sq. no have odd number of factors

    • 2 years ago
  27. shubhamsrg Group Title
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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

    • 2 years ago
  28. shubhamsrg Group Title
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    damn i closed the quess,,wait i shall tag,,

    • 2 years ago
  29. shubhamsrg Group Title
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    @mukushla @eliassaab

    • 2 years ago
  30. sauravshakya Group Title
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    Oh..... got it....... I think I can prove it

    • 2 years ago
  31. sauravshakya Group Title
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    IF its not an sq. number.... for example 12 then the factors are 1,2,3,4,6,12

    • 2 years ago
  32. sauravshakya Group Title
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    right?

    • 2 years ago
  33. shubhamsrg Group Title
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    yes..

    • 2 years ago
  34. sauravshakya Group Title
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    |dw:1345558048314:dw|Now,

    • 2 years ago
  35. sauravshakya Group Title
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    Now, lets look a sq. number ... for example 25 its factors are 1,5,5,25|dw:1345558167578:dw|

    • 2 years ago
  36. shubhamsrg Group Title
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    hmm..so every no. will have even no. of factors if we count same no. twice..really ? that quite amazing!

    • 2 years ago
  37. sauravshakya Group Title
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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

    • 2 years ago
  38. sauravshakya Group Title
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    TO make it more clear......|dw:1345558421778:dw|

    • 2 years ago
  39. sauravshakya Group Title
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    and sum of even numbers is always a even number

    • 2 years ago
  40. shubhamsrg Group Title
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    cool..i get it! nice.. :)

    • 2 years ago
  41. shubhamsrg Group Title
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    now lets return to my ques,,why only sq. nos should be there?

    • 2 years ago
  42. sauravshakya Group Title
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    To...... write and make other understand is a very difficult......

    • 2 years ago
  43. sauravshakya Group Title
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    without speaking

    • 2 years ago
  44. sauravshakya Group Title
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    Am i right?

    • 2 years ago
  45. shubhamsrg Group Title
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    lol..you did a pretty good job sir.,thanks..

    • 2 years ago
  46. sauravshakya Group Title
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    I mean it is easy for u guys........... but for others its really hard

    • 2 years ago
  47. shubhamsrg Group Title
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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?

    • 2 years ago
  48. mukushla Group Title
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    *bookmark

    • 2 years ago
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