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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?

  • one year ago
  • one year ago

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

    • one year 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)

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

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

    • one year ago
  5. lgbasallote Group Title
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    yes it will

    • one year ago
  6. lgbasallote Group Title
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    1 is a perfect square isnt it

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

    • one year ago
  8. Yahoo! Group Title
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    100 th room

    • one year ago
  9. lgbasallote Group Title
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    for 9 1 opens 9 3 closes 9 9 opens 9

    • one year 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

    • one year ago
  11. lgbasallote Group Title
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    for 25 1 opens 25 5 closes 25 25 opens 25

    • one year 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

    • one year ago
  13. lgbasallote Group Title
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    for 49 1 opens 49 7 closes 49 49 opens 49

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

    • one year 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..

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

    • one year 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

    • one year ago
  18. lgbasallote Group Title
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    what comesafter 64 again?

    • one year ago
  19. shubhamsrg Group Title
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    81 1o 3c 9o 27c 81o

    • one year ago
  20. lgbasallote Group Title
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    yes that

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

    • one year ago
  22. lgbasallote Group Title
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    welcome

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

    • one year ago
  24. lgbasallote Group Title
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    it's a tedious proof... lol

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

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

    • one year 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

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

    • one year ago
  29. shubhamsrg Group Title
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    @mukushla @eliassaab

    • one year ago
  30. sauravshakya Group Title
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    Oh..... got it....... I think I can prove it

    • one year 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

    • one year ago
  32. sauravshakya Group Title
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    right?

    • one year ago
  33. shubhamsrg Group Title
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    yes..

    • one year ago
  34. sauravshakya Group Title
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    |dw:1345558048314:dw|Now,

    • one year 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|

    • one year 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!

    • one year 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

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

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

    • one year ago
  40. shubhamsrg Group Title
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    cool..i get it! nice.. :)

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

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

    • one year ago
  43. sauravshakya Group Title
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    without speaking

    • one year ago
  44. sauravshakya Group Title
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    Am i right?

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

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

    • one year 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?

    • one year ago
  48. mukushla Group Title
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    *bookmark

    • one year ago
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