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imqwerty
 one year ago
Fun question
imqwerty
 one year ago
Fun question

This Question is Closed

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.1U 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 ishow many valleys will be formed if u fold the paper half 9 times.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You fold it 9 times, but do you always switch directions when folding?

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.1No u can't switch directions while folding. U have to fold along the same directions.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If you fold along the same direction, then your second fold should give you 3 valleys.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Your valleys will be parallel

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.1Wait I am sending a pic of valleys nd hills formed after folding the paper twice

myininaya
 one year ago
Best ResponseYou've already chosen the best response.0errr my paper won't let me fold it more than 5 times :p

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0reminds me of Alice in wonderland

dan815
 one year ago
Best ResponseYou've already chosen the best response.0which way am i folding it in half

myininaya
 one year ago
Best ResponseYou've already chosen the best response.0for 5 folds I get: 8 valleys 8 hills I think maybe we can find a pattern like you know 2,3,4 folds...

dan815
 one year ago
Best ResponseYou've already chosen the best response.0whats a valley, whats a hill, im confused

myininaya
 one year ago
Best ResponseYou've already chosen the best response.0the paper touches the desk=valley the paper doesn't touch the desk=hill

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0dw:1436162117710:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm getting about \(2^{n1}\) values and \(2^{n1}1\) hills.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.0my hills and valleys are becoming hard to read

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[ \begin{array}{ccc} \text{folds} & \text{valleys} & \text{hills} \\ \hline 1&1&0\\ 2&2&1\\ 3&4&3\\ 4&8&7\\ 5&16&15\\ 6&32&31\\ 7&64&63\\ 8&128&127\\ 9&256&255 \end{array} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm going to experiment a bit more though

myininaya
 one year ago
Best ResponseYou've already chosen the best response.0for 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)

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.1u got the correct answer @wio

myininaya
 one year ago
Best ResponseYou've already chosen the best response.0my paper isn't working :p

myininaya
 one year ago
Best ResponseYou've already chosen the best response.0I can't get the same thing they had for 2 folds :p

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Think 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

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0is the setup somehow similar to dw:1436162688519:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's clear that after 9 folds, you'll have \(2^9\) sections, divided by \(2^91\) 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 \((2^92)/2 = 2^81 = 255\). The number of valleys is just hills plus one \(255 + 1 = 256\).

myininaya
 one year ago
Best ResponseYou've already chosen the best response.0hey 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 / ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1436162935382:dw

myininaya
 one year ago
Best ResponseYou've already chosen the best response.0and we don't consider the endpoints

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0i think we count only the new creases formed

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.1wio is absolutely correct

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0First I thought it was like this: dw:1436163027686:dw

dan815
 one year ago
Best ResponseYou've already chosen the best response.0thats what im working with, is that wrong way to fold

myininaya
 one year ago
Best ResponseYou've already chosen the best response.0so for 3 folds I have: dw:1436163142668:dw

dan815
 one year ago
Best ResponseYou've already chosen the best response.0you are still creating the same number of valley and hills with every fold except the first fold

myininaya
 one year ago
Best ResponseYou've already chosen the best response.0oh yeah that checks out :)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0dw:1436163257855:dw

dan815
 one year ago
Best ResponseYou've already chosen the best response.0ah xD im already working on the other problem though its interesting

dan815
 one year ago
Best ResponseYou've already chosen the best response.0i think the solution might be the same if you fold this way too dw:1436163499857:dw

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.1ok 1 fold1valley 2 folds2 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

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.1u 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

dan815
 one year ago
Best ResponseYou've already chosen the best response.0they 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

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0so after n alternate folds, the paper gets dividied into 2^n parts

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The points are given by horizontal and vertical folds

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.1@dan815 according to the question a hill is this kind of structure dw:1436250404384:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0with alternate folds we may define hill as convex and valley as concave

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.1okay but the question is not saying to do so.

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.1i got some more interesting questions which are even more fun than this one.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.0dw:1436164431433:dw isn't this picture representing one hit and two valleys? it isn't just one structure right?

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.1yes the pic represents *1hill between 2 valleys

myininaya
 one year ago
Best ResponseYou've already chosen the best response.0ok cool I just wanted to make sure I was happy with my understanding :)
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