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imqwerty

  • one year ago

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  1. imqwerty
    • one year ago
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    U got a paper and u fold it half and then u open it and when u open it u will see a valley type of thing formed(V). If u fold the paper half twice along the same length and then open it u'll see 2valleys(V) and 1hill(^) formed. Now the question is-how many valleys will be formed if u fold the paper half 9 times.

  2. imqwerty
    • one year ago
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    @butterflydreamer

  3. anonymous
    • one year ago
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    You fold it 9 times, but do you always switch directions when folding?

  4. imqwerty
    • one year ago
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    No u can't switch directions while folding. U have to fold along the same directions.

  5. anonymous
    • one year ago
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    If you fold along the same direction, then your second fold should give you 3 valleys.

  6. anonymous
    • one year ago
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    Your valleys will be parallel

  7. imqwerty
    • one year ago
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    Wait I am sending a pic of valleys nd hills formed after folding the paper twice

  8. myininaya
    • one year ago
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    errr my paper won't let me fold it more than 5 times :p

  9. ganeshie8
    • one year ago
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    reminds me of Alice in wonderland

  10. imqwerty
    • one year ago
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    Lol

  11. dan815
    • one year ago
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    which way am i folding it in half

  12. dan815
    • one year ago
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    |dw:1436161935981:dw|

  13. myininaya
    • one year ago
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    for 5 folds I get: 8 valleys 8 hills I think maybe we can find a pattern like you know 2,3,4 folds...

  14. dan815
    • one year ago
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    whats a valley, whats a hill, im confused

  15. myininaya
    • one year ago
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    the paper touches the desk=valley the paper doesn't touch the desk=hill

  16. imqwerty
    • one year ago
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    Exactly

  17. dan815
    • one year ago
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    ahh ok

  18. ganeshie8
    • one year ago
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    |dw:1436162117710:dw|

  19. anonymous
    • one year ago
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    I'm getting about \(2^{n-1}\) values and \(2^{n-1}-1\) hills.

  20. myininaya
    • one year ago
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    my hills and valleys are becoming hard to read

  21. anonymous
    • one year ago
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    \[ \begin{array}{c|c|c} \text{folds} & \text{valleys} & \text{hills} \\ \hline 1&1&0\\ 2&2&1\\ 3&4&3\\ 4&8&7\\ 5&16&15\\ 6&32&31\\ 7&64&63\\ 8&128&127\\ 9&256&255 \end{array} \]

  22. anonymous
    • one year ago
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    I'm going to experiment a bit more though

  23. myininaya
    • one year ago
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    for 3 folds... I'm getting 2 valleys and 2 and half hills (I say two and a half because the end of my paper is standing up but the hill doesn't end because the paper does end; to me it isn't a complete hill)

  24. imqwerty
    • one year ago
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    u got the correct answer @wio

  25. myininaya
    • one year ago
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    my paper isn't working :p

  26. myininaya
    • one year ago
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    I can't get the same thing they had for 2 folds :p

  27. anonymous
    • one year ago
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    Think of a paper for which the front side is red and the back side is blue. On you first fold, you have just the red side showing up, so you create a valley On the second fold, you have a red side and a blue side on top, so you create a valley and a hill. On the third fold, you have red, blue, red, blue. This means you're creating two more values and two more hills. The way you fold it, there will always be the same number or reds and blues (except at the very start), so you'll always create the same amount hills and valleys with exception of the head start at the beginning

  28. ganeshie8
    • one year ago
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    is the setup somehow similar to |dw:1436162688519:dw|

  29. anonymous
    • one year ago
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    It's clear that after 9 folds, you'll have \(2^9\) sections, divided by \(2^9-1\) creases. It's clear this is an odd number of creases. Subtract it be one and divide by two to get the number of hills \((2^9-2)/2 = 2^8-1 = 255\). The number of valleys is just hills plus one \(255 + 1 = 256\).

  30. myininaya
    • one year ago
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    hey for two folds I have this: |dw:1436162856530:dw| how should I read this like the ^ is a hill to me _ is a valley to me but what about the / ?

  31. anonymous
    • one year ago
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    |dw:1436162935382:dw|

  32. myininaya
    • one year ago
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    oh the points

  33. myininaya
    • one year ago
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    and we don't consider the endpoints

  34. ganeshie8
    • one year ago
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    i think we count only the new creases formed

  35. imqwerty
    • one year ago
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    wio is absolutely correct

  36. anonymous
    • one year ago
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    First I thought it was like this: |dw:1436163027686:dw|

  37. dan815
    • one year ago
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    thats what im working with, is that wrong way to fold

  38. myininaya
    • one year ago
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    so for 3 folds I have: |dw:1436163142668:dw|

  39. dan815
    • one year ago
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    you are still creating the same number of valley and hills with every fold except the first fold

  40. myininaya
    • one year ago
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    oh yeah that checks out :)

  41. ganeshie8
    • one year ago
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    |dw:1436163257855:dw|

  42. dan815
    • one year ago
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    ah xD im already working on the other problem though its interesting

  43. imqwerty
    • one year ago
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  44. dan815
    • one year ago
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    i think the solution might be the same if you fold this way too |dw:1436163499857:dw|

  45. imqwerty
    • one year ago
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    ok 1 fold-1valley 2 folds-2 valleys 1hill 3folds - 4vallyes 3hill 4folds- 8valleys 7hills we observe that always the no. of valleys is one more than the no. of hill and also that the sum of valleys+hills=2^(no. of folds) -1 so with this info we can find the no. of valleys after 9 folds

  46. imqwerty
    • one year ago
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    u can fold the paper along the x axis or along the y axis but u cant flip directions because then hills and valleys won't form

  47. dan815
    • one year ago
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    they still do form, but you have to define what is a hill because u can have the same hill span through multiple points, but if u define a hill or valley to be inbetween the intsersections of the folds

  48. dan815
    • one year ago
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    |dw:1436163851891:dw|

  49. ganeshie8
    • one year ago
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    so after n alternate folds, the paper gets dividied into 2^n parts

  50. anonymous
    • one year ago
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    The points are given by horizontal and vertical folds

  51. imqwerty
    • one year ago
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    @dan815 according to the question a hill is this kind of structure- |dw:1436250404384:dw|

  52. ganeshie8
    • one year ago
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    with alternate folds we may define hill as convex and valley as concave

  53. imqwerty
    • one year ago
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    okay but the question is not saying to do so.

  54. imqwerty
    • one year ago
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    i got some more interesting questions which are even more fun than this one.

  55. myininaya
    • one year ago
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    |dw:1436164431433:dw| isn't this picture representing one hit and two valleys? it isn't just one structure right?

  56. myininaya
    • one year ago
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    one hill*

  57. imqwerty
    • one year ago
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    yes the pic represents *1hill between 2 valleys

  58. myininaya
    • one year ago
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    ok cool I just wanted to make sure I was happy with my understanding :)

  59. imqwerty
    • one year ago
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    ( ͡° ͜ʖ ͡°)

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