A Nifty Puzzle

[pneu-engine]

I LOOOOOOOOOOOOOOOOOOVE the beauty of mathematics :Green

Here is a really neat puzzle for your perusal::::::::::::::::


Take a full-size sheet of paper and cut it in half.

Place the cutoff half on top of the other half so that now there are two pieces of paper one on top of the other.

Cut the two-piece stack in half and place the cutoff pieces on top of the other two just as you did previously.

Cut he four-piece stack in half and place the four cutoff pieces on top of the other four pieces.

Do it again.

...and again

...and again

...keep doing that until you have done that a total of ten times.

Now for the question:::::::::::::::::;;

***Since ordinary bond paper is approx. 3-1/2 mils thick (i.e. 0.0035"), how high would your stack be at the end of the tenth cycle (a cycle = cut 'n' re-stack).

***If you did that for 20 cycles how high would your stack be?

***How high after 30 cycles? ...after forty cycles? ...after fifty cycles? ...after 100 cycles?

The answers are truly amazing. It just shows to go ya the power of God and the beauty that He created into mathematics.

[pneu-engine]

I LOOOOOOOOOOOOOOOOOOVE the beauty of mathematics :Green

Here is a really neat puzzle for your perusal::::::::::::::::


Take a full-size sheet of paper and cut it in half.

Place the cutoff half on top of the other half so that now there are two pieces of paper one on top of the other.

Cut the two-piece stack in half and place the cutoff pieces on top of the other two just as you did previously.

Cut he four-piece stack in half and place the four cutoff pieces on top of the other four pieces.

Do it again.

...and again

...and again

...keep doing that until you have done that a total of ten times.

Now for the question:::::::::::::::::;;

***Since ordinary bond paper is approx. 3-1/2 mils thick (i.e. 0.0035"), how high would your stack be at the end of the tenth cycle (a cycle = cut 'n' re-stack).

***If you did that for 20 cycles how high would your stack be?

***How high after 30 cycles? ...after forty cycles? ...after fifty cycles? ...after 100 cycles?

The answers are truly amazing. It just shows to go ya the power of God and the beauty that He created into mathematics.

It's time for the answers. :Green

After ten cuts the stack contains 1,024 pieces and is ~3.5 inches high.

After 20 cuts the stack is 1,048, 576 pcs and is about ~3,670 inches high or ~305 feet.

After 30 cuts the stack is more than a billion pcs and is over 59 miles high.

After 40 cuts the stack is more than a trillion pcs and is ~60,000 miles high.

After 50 cuts the stack is two thirds of the way to the sun or ~ 62 million miles.

After 100 cuts the stack goes 28 times farther out into the deep sky than the visible universe.

[Bakershalfdozen]

Just considering that puzzle made me dizzy. Also, if I were to cut a piece of paper that many times there wouldn't be anything left. :Green Just kidding - I know it is a math puzzle, not a physics puzzle.

[pneu-engine]

Just considering that puzzle made me dizzy. Also' date=' if I were to cut a piece of paper that many times there wouldn't be anything left. :Green Just kidding - I know it is a math puzzle, not a physics puzzle.[/quote']
:Green I was hoping somebody would point out the fact that by the 30th cut the pieces would be almost too small to be seen and by the 100th cut they would be very nearly microscopic.

Not only that but to get 1,000,000,000 pcs of paper (the 30th cut) to stand in a single stack would be wonderfully difficult.

[HappyChristian]

And all of that from one sheet of paper! :Green

[Guest Guest]

Your an engineer aren't you? Great puzzle thanks! Just glad you solved it for me! :puzzled: Pixiedust

[pneu-engine]

:Green