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shubhamsrg

  • 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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  1. shubhamsrg
    • 2 years ago
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    i dont know! :P any good reasons ?

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

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

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

  5. lgbasallote
    • 2 years ago
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    yes it will

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

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

  8. Yahoo!
    • 2 years ago
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    100 th room

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

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

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

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

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

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

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

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

  17. lgbasallote
    • 2 years ago
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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

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

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

  20. lgbasallote
    • 2 years ago
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    yes that

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

  22. lgbasallote
    • 2 years ago
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    welcome

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

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

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

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

  27. shubhamsrg
    • 2 years ago
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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

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

  29. shubhamsrg
    • 2 years ago
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    @mukushla @eliassaab

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

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

  32. sauravshakya
    • 2 years ago
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    right?

  33. shubhamsrg
    • 2 years ago
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    yes..

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

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

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

  37. sauravshakya
    • 2 years ago
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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

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

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

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

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

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

  43. sauravshakya
    • 2 years ago
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    without speaking

  44. sauravshakya
    • 2 years ago
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    Am i right?

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

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

  47. shubhamsrg
    • 2 years ago
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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?

  48. mukushla
    • 2 years ago
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    *bookmark

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