Fun brain teaser

[clintonnut 126]

Ok, i know this is impossible to do but if you could fold a dollar bill 50 times, how thick would it be? A bill is .003" thick. So,

1 fold would make it .006

2 folds would make it .012

3 folds would make it .024

4 folds would make it .048

5 folds would make it .096

If you know much about exponents you should notice something about the thickness as it is folded each additional time. So the choices are:

50"

50'

50 miles

50,000,000 miles

If you get it right simply explain for those that dont get it.

Charlie

[dkopp 1]

Oh goody, an engineering problem.

use the following formula where T is the total thickness

and t is the initial thickness of the dollar bill (0.003 inches)

Let n equal the number of folds

now the thickness added to each fold is double the previous thickness but dependent

upon the number of the previous folds

So...

Our formula should be T(n# of folds)=2^n*t or T(n) = 2^n* 0.003

Let's try it to see if it works:

Initial fold n=1

T= 2^1 * 0.003 T=0.006 inches thick Works with that one!

Let's try 3 folds: n=3

T = 2^3 * 0.003 2^3 = 8 so... 8 * 0.003 = 0.024 inches thick It works!

Let's go for the big 'un: 50 folds ... n=50

T(n=50) = 2^50 * 0.003 2^50 = 1.125899907 x 10^15

(1.125899907 x 10^15) * 0.003 = 3.377699721 x 10^12 inches thick

way to big of a number to deal with... so let's convert that to something a little more reasonable....

Converting to feet will still be too big.... let's try miles (63,360 inches per mile)

3.377699721 x 10^12 inches / 63,360 inches per mile = 53,309,654.68 miles

[clintonnut 126]

You hit the nail on the head!

[rmaynard 15,937]

I'm still trying to fold my dollar bill...

[dkopp 1]

Good brain teaser Charlie! Brings me back to the ol' college days. You know you get too far into math when they stop using numbers and you can come up with a formula using nothing but letters. No wonder I can't balance my checkbook.

Current working hours x current pay rate x hours worked - bills and life = broke :banghead:

[MikesRJ 555]

Just a touch over 53,309,651.680 miles

[rmaynard 15,937]

Hey teacher, Mike looked at Dan's paper. :banghead:

[chesbaycruiser 83]

I just worked this out on the computer in Excel so you could see the change line by line. I started out with "inches", then changed to "feet", then "miles" as the thickness increased. Then I brought my two youngest sons (12 & 13) in and posed the riddle to them.

Once they had guessed (1/2" and 8"), I slowly scrolled down the list of numbers, revealing one line at a time. They got a huge kick out of it...getting more and more excited as we went up each major milestone...feet to miles to hundreds then thousands then millions!

The 13 yr old (who was playing video games online) was so impressed he immediately had to pose the question to all his "online friends"!

Thanks for the fun diversion!

Fold # Thickness Unit

0.003 Inches

1 0.006 Inches

2 0.012 Inches

3 0.024 Inches

4 0.048 Inches

5 0.096 Inches

6 0.192 Inches

7 0.384 Inches

8 0.768 Inches

9 1.536 Inches

10 3.072 Inches

11 6.144 Inches

12 1.024 Feet

13 2.048 Feet

14 4.096 Feet

15 8.192 Feet

16 16.38 Feet

17 32.77 Feet

18 65.54 Feet

19 131.07 Feet

20 262.14 Feet

21 524.29 Feet

22 1048.58 Feet

23 2097.15 Feet

24 4194.30 Feet

25 1.6 Miles

26 3.2 Miles

27 6.4 Miles

28 12.7 Miles

29 25 Miles

30 51 Miles

31 102 Miles

32 203 Miles

33 407 Miles

34 813 Miles

35 1627 Miles

36 3254 Miles

37 6508 Miles

38 13015 Miles

39 26030 Miles

40 52060 Miles

41 104120 Miles

42 208241 Miles

43 416482 Miles

44 832963 Miles

45 1665927 Miles

46 3331853 Miles

47 6663707 Miles

48 13327414 Miles

49 26654827 Miles

50 53309655 Miles

[d180man 5]

I'm still trying to fold my dollar bill...

Hi me too ! :ROTF:

[flyovrcntry 115]

O>K> what about a 10 dollar bill ?

I think it's a hundred times as much :thumbs:

[marvairplanes 34]

Kinda' like the story of the fella who invented the game CHECKERS.

The king was so impressed that he promised, as a reward to the inventor, anything he wished for, up to "half of my kingdom".

The inventor, who didn't want to seem greedy replied, "just give me a grain of wheat on the first square, 2 grains on the second, 4 on the next, and just keep doubling the number of grains on each of the remaining squares."

King thought he got a real bargain, and said "agreed". He called for a bushel of wheat, but soon ran out of grains, and called for a second bushel.

Result...it would take EVERY grain of wheat that has EVER been grown in every country of the world, since DAY 1, and every grain that will be produced in the next 1000 years, and there still wouldn't be enough for all 64 squares.

Go figure !!!!

I gave this problem as an assignment to one of my Advanced Math classes when I was still teaching 20 some years ago. ????? Wonder if they are still working on it ????

Marv

NW Oh

[clintonnut 126]

Another fun one is how tall of a pile of $100 bills would equal our national debt!

Dollar bill is .003

National debt is around $14,000,000,000,000,000,000 (14 trillion) hard to estimate because it keeps getting bigger!

Charlie

[JimD 3,345]

53,309,654.68 miles. Hey, I took a shot. :banghead:

[rmaynard 15,937]

Based on a debt of $14,000,000,000,000 (14 Trillion), the pile would be 662,878.788 miles high.

[6wheeler 668]

Hey, can I borrow a dollar? I got a trick to show ya :banghead:

[linen beige 14]

Ok, i know this is impossible to do but if you could fold a dollar bill 50 times, how thick would it be? A bill is .003" thick.

It isn't impossible.

The answer is 0.015 inches.

folded accordion style. :thumbs:

[dkopp 1]

Kinda' like the story of the fella who invented the game CHECKERS.

The king was so impressed that he promised, as a reward to the inventor, anything he wished for, up to "half of my kingdom".

The inventor, who didn't want to seem greedy replied, "just give me a grain of wheat on the first square, 2 grains on the second, 4 on the next, and just keep doubling the number of grains on each of the remaining squares."

King thought he got a real bargain, and said "agreed". He called for a bushel of wheat, but soon ran out of grains, and called for a second bushel.

Result...it would take EVERY grain of wheat that has EVER been grown in every country of the world, since DAY 1, and every grain that will be produced in the next 1000 years, and there still wouldn't be enough for all 64 squares.

Go figure !!!!

I gave this problem as an assignment to one of my Advanced Math classes when I was still teaching 20 some years ago. ????? Wonder if they are still working on it ????

Marv

NW Oh

To be more precise, it would take close to 922,337,204 years to produce the amount for that wager.

Using the following numbers:

2^64 = 1.8447 x 10^19

1 bushel of wheat has about 1,000,000 kernels

An average bushel of wheat weighs about 60 lbs.

The average annual production of wheat in 2007 was about 600 tons worldwide.

Of course it would take longer due to droughts and other unforeseen issues.

[TT-(Moderator) 1,147]

Ok, i know this is impossible to do but if you could fold a dollar bill 50 times, how thick would it be? A bill is .003" thick.

It isn't impossible.

The answer is 0.015 inches.

folded accordion style.

It's a trick question anyhow......

No matter how many times you fold it, twist it, crumple it, etc., a dollar bill is still only .0043" thick - even with inflation. :thumbs:

[chesbaycruiser 83]

The average annual production of wheat in 2007 was about 600 tons worldwide.

Methinks that's a typo!?!?

Wheat Production for 2008/09

World -- 282.67 Million Metric Tons

US -- 68.02 Million Metric Tons

http://www.fas.usda.gov/psdonline/psdgetre...valTemplateID=1

:thumbs:

[linen beige 14]

Ok, i know this is impossible to do but if you could fold a dollar bill 50 times, how thick would it be? A bill is .003" thick.

It isn't impossible.

The answer is 0.015 inches.

folded accordion style.

It's a trick question anyhow......

No matter how many times you fold it, twist it, crumple it, etc., a dollar bill is still only .0043" thick - even with inflation.

:hide:

[dkopp 1]

Yup, that's a bad number...sorry about that folks. Thanks for the correct numbers and the link Chris.

Pays to double check your sources. I wanted to convert grains to bushels since wheat is mainly dealt with in bushels and not grains and that number was published on a web site I found, but not correct, my mistake.

[GlenPettit 1,717]

I love playing with numbers:

Take the last two digits of the year you were born and add that to your age this year,

you will always get 111.

And another ONE this year, we have: 1/1/11, 1/11/11, 11/1/11 and 11/11/11

[chesbaycruiser 83]

Take the last two digits of the year you were born and add that to your age this year, you will always get 111.

Unless....you were born in 2000 or later...then it always equals 11!

:banghead: