Fun Brain Teaser -- Revisited

[chesbaycruiser 82]

I got to thinking about this riddle some more, and given how thick the bill became as it expanded exponentially, the inverse should also be true regarding the area of the bill as it gets smaller with each fold.

Using my remedial math skills, I think the inverse of this riddle is pretty spectacular as well. Here's what I came up with. (Please, some of you math experts, check my logic/process/math!!!)

A standard US bill is about 6 1/16" x 2 9/16" (6.0625" x 2.5625")

The first fold makes it 3 1/32" x 2 9/16" (3.03125 x x 2.5625")

The second fold makes it 3 1/32" x 1 17/64" (3.03125 x x 1.28125")

And so on....

Just like with the thickness riddle, the dimensions quickly become unmanageable using inches, so I ended up converting to Microns. A micron is one millionth of a meter. It takes 24.5 microns to equal .001", or put another way 24,500 microns equal one inch. By comparison, a human hair is typically 40 - 120 microns, and a period on this page is about 395 microns. So, now armed with all that trivial knowledge....

The final dimensions of the bill after the 50th fold would be: .004589 x .001939 Microns

Wow...that's a tiny little rectangle! To get some perspective on how small that is....using our folded bill's "widest" dimension of .004589 microns, it would take about 217 folded bills to equal the "width" of one micron [217 x .0045 = 1]. Likewise, using the folded bills smaller dimension of .001939, it would take 515 folded bills to equal one micron in height (515 x .0019 = 1). That creates a one micron "square" made up of 112,335 folded bills (217 x 515 = 112,335)

So, assuming a micron is round, how does that translate? (For the record, here's where I start moving out of my math comfort zone...I'll call this an educated guesstimate. Feel free to point out my errors!)

If we divide our square into quarters, we get four squares with an area of 28.084 "bills" each. Using the graphic above, we multiply the area of one of those squares by Pi to get the total area of our circle (one micron)....so 28,084 x 3.14 = an area of 88,183 folded bills in one micron.

So, to achieve the size of a single period on this page (88,183 bills x 395 microns), we would need approximately 34,832,406 folded bills!!!! ) (One of you math wizards out there should probably check my work!)

(FYI...the dollar bill we started out with has an area of 10,022,661,406 microns. I can't tell you how many folded bills that works out to, other than it's 1.12008E+15, which is a hell of a lot! )

To quote the rock band Styx: "...too much time on my hands..." :ROTF:

[marvairplanes 34]

"If we divide our square into quarters, we get four squares with an area of 28.084 "bills" each. Using the graphic above, we multiply the area of one of those squares by Pi to get the total area of our circle (one micron)....so 28,084 x 3.14 = an area of 88,183 folded bills in one micron."

You used the pretty common value of pi...3.14.

If we would use 3.141592653589, your calculations would be effected...well, at least a little bit.

That value above, if working with a circle the size of the diameter of the earth, will give results correct to 1/1,000,000 of an inch. Guess that would be close enough !

Marv

[Kelly 1,028]

:banghead: :thumbs:

[sscotsman 132]

So..to combine the two riddles, after you have folded your dollar bill 50 times,

it is about the size of an atom wide, and 50,000,000 miles thick..

cool!

Scot

[stoneman 10]

so . . . if you took that atoms width, 50,000,000 mile microscopic thread, created from a dollar bill, and rolled it into a ball, how round would it be? :banghead:

[sscotsman 132]

so . . . if you took that atoms width, 50,000,000 mile microscopic thread, created from a dollar bill, and rolled it into a ball, how round would it be?

it would be about the same size as taking a normal dollar bill and wadding it up into a ball!

even though its an atom wide and 50,000,000 miles long, its mass hasnt changed..

you could probably make a smaller ball using the 50,000,000 mile long version, because you could wind it much tighter..while just wadding up a normal dollar you have a lot of air space..but still, they are the same mass.

Scot

[stoneman 10]

so . . . if you took that atoms width, 50,000,000 mile microscopic thread, created from a dollar bill, and rolled it into a ball, how round would it be?

it would be about the same size as taking a normal dollar bill and wadding it up into a ball!

even though its an atom wide and 50,000,000 miles long, its mass hasnt changed..

Scot

uh . . .okay . . . but, how round would it be? :ROTF:

[sscotsman 132]

so . . . if you took that atoms width, 50,000,000 mile microscopic thread, created from a dollar bill, and rolled it into a ball, how round would it be?

it would be about the same size as taking a normal dollar bill and wadding it up into a ball!

even though its an atom wide and 50,000,000 miles long, its mass hasnt changed..

Scot

uh . . .okay . . . but, how round would it be?

that one is probably *truly* imposibe to figure out!

you would have to start with a ball 1-atom across..then increase the width by one atom every time you wind another layer..and as you continue to wind, you have more and more "strings" on each layer...and overlapping layers..

(just like winding up a ball of string, but with 50,000,000 miles of string!)

I think we have truly reached the realm of impossibility with that one!

(although if someone wants to give it a try!

Scot

[stoneman 10]

so . . . if you took that atoms width, 50,000,000 mile microscopic thread, created from a dollar bill, and rolled it into a ball, how round would it be?

it would be about the same size as taking a normal dollar bill and wadding it up into a ball!

even though its an atom wide and 50,000,000 miles long, its mass hasnt changed..

Scot

uh . . .okay . . . but, how round would it be?

that one is probably *truly* imposibe to figure out!

you would have to start with a ball 1-atom across..then increase the width by one atom every time you wind another layer..and as you continue to wind, you have more and more "strings" on each layer...and overlapping layers..

(just like winding up a ball of string, but with 50,000,000 miles of string!)

I think we have truly reached the realm of impossibility with that one!

(although if someone wants to give it a try!

Scot

i think it would have to depend on who was winding it up. and then there would be all kinds of variables . . . like what methodology they would be using, will they be drinking while they are doing it . . . and if so . . . what . . . and how often. how tight would they roll it, or how loose. and i wonder what would take longer . . . bending the bill 50 times or rolling it up into a ball. :thumbs:

[Duff 206]

The question posed was, "How round would it be?" The answer is simple - round is round. Period!

Now if you had asked, "If you roll it into a ball, what would the diameter of the ball be?" then we can go off on a whole tangent of calculations!

Duff :thumbs:

[stoneman 10]

The question posed was, "How round would it be?" The answer is simple - round is round. Period!

Now if you had asked, "If you roll it into a ball, what would the diameter of the ball be?" then we can go off on a whole tangent of calculations!

Duff

. . . or the circumference . Perhaps this would apply.

AB = Diameter

Must pass through the centre of the circle. The Diameter is equal to twice the radius.

OC = Radius

The radius is a line segment that begin from the centre and touches any point on the circle.

ED = Chord

The chord joins any two points on a circle.

FG = Tangent

A line with one point common to the circle.

EHD = Arc

Only the portion of the circle that is between two points on the circle.

ADB = Semicircle

Also considered to be an arc that is exactly half of the circle.

OCB = Sector

The area between two radii and the arc.

COB = Central Angle

Fromed by two radii. :banghead:

[Jim_M 178]

Just send your dollar bills to me and I'll get back to you with the answers.

[just me 0]

You can only fold it so many times before it becomes impossible to fold any more. I do believe its something in the teens.

[chesbaycruiser 82]

You can only fold it so many times before it becomes impossible to fold any more. I do believe its something in the teens.

You are correct that this is physically impossible. It was established in the first post (here) that this riddle that this is only hypothetical.

Actually, I'd be surprised if you can actually fold it much more than 4 or 5 times....

Besides, once the folded bill got much past a million miles, I think my arms would be pretty tired! :banghead:

[just me 0]

sorry didn't realize it was already brought up. I should read all before I put my 2 cents in

[sscotsman 132]

The story is "you cant fold a piece of paper more than seven times"

(try it!)

Mythbusters tackled it, and were able to get more than 7 folds:

Scot

[just me 0]

So its 7 I thought it was 13. So why are we discussing this then. Just so you can show you know how to add?

[chesbaycruiser 82]

So its 7 I thought it was 13. So why are we discussing this then. Just so you can show you know how to add?

Well THAT was totally uncalled for.

[sscotsman 132]

So its 7 I thought it was 13. So why are we discussing this then. Just so you can show you know how to add?

Well THAT was totally uncalled for.

and also completely missing the point!

oh well..

Scot

[just me 0]

Ok what is the point?

[sscotsman 132]

Ok what is the point?

"Just me"

There are two threads about this "math problem"..

Here is the first one:

http://www.wheelhorseforum.com/index.php?showtopic=24996

this is the second one..

"the point" is stated in the subject lines of both threads..

and I think I now understand where you made a wrong turn..

I think that perhaps you thought when I posted:

The story is "you cant fold a piece of paper more than seven times"

(try it!)

Mythbusters tackled it, and were able to get more than 7 folds:

Scot

that I was speaking directly to you personally.

I was not..

I was speaking to "the group" in general..speaking to "the thread"..

just adding a new small interesting bit of fun to the topic..

I didnt even notice that you said 13!

but your post reminded me of the mythbusters bit..so I posted it.

I think maybe you took offense where none was intended..but there was no offence meant.

Scot

[just me 0]

really no offense taken at all I just don't get this topic. Is it to try to show that you may be more educated than others or that you can scratch out some equations and show that you may know something that someone does not. Although a very fascinating subject that I learned about in grade school I now find to be boring. And yes I don't have to read but I do cause my life really is that boring

[sscotsman 132]

well..sorry "Just me"..

I dont know what to tell you then..

(and now I cant tell if you are speaking to me personally, or to everyone in general..but it doesnt really matter..)

If you dont like the thread, then just move along I guess..

sorry our fun topic caused you such boredom.

Scot

[6wheeler 586]

Where do you fellas come up with this stuff? I for one, am just happy if I fold a dollar once and the ends line up . I know where I am going if I have a math problem from now on. You guys are smart. And, I mean that as a compliment.. Jim, if you start getting dollars in the mail, please feel free to forward the extras to me . Keep up the riddles fellas, they are fun to read.. Pat

[chesbaycruiser 82]

....I just don't get this topic. Is it to try to show that you may be more educated than others or that you can scratch out some equations and show that you may know something that someone does not. Although a very fascinating subject that I learned about in grade school I now find to be boring. And yes I don't have to read but I do cause my life really is that boring

Seriously? Are you this sensitive about everything?

I know you've only been a member here for a day, but I have to tell you....if you're gonna' get your undies in a bunch every time someone posts something you don't personally find interesting, or when they lay on some thick techno-jargon you're gonna' take personal offense because you think they're trying to talk over your head....I don't think you're going to like it here very much.

This place is a great resource. If you have a question, ask it and someone here will probably have an answer. Other times, you might have an answer for someone else. Got a story to tell....folks here will listen. Make a mistake, someone will probably call you on it. But one thing is for sure....there are literally hundreds of thousands of posts here, and I assure you that not EVERY one of them will be interesting to you, no matter how boring you claim your life is.

And I promise you this: if you wade into a pleasant conversation that started before you ever signed up and sh*t all over it for no good reason, it won't ever go over very well. In the case of this post, the title clearly says "Brain Teaser". I'm assuming you know what that means, so if it's not your cup of tea, then skip it, and spare everyone the insults and petulant comments. I think you'll find the folks in RedSquare have better manners than that.