Poll

No votes (0%)
No votes (0%)
2 votes (66.66%)
No votes (0%)
1 vote (33.33%)
No votes (0%)
No votes (0%)
1 vote (33.33%)
3 votes (100%)
No votes (0%)

3 members have voted

Wizard
Administrator
Wizard
Joined: Oct 14, 2009
  • Threads: 1390
  • Posts: 23442
March 16th, 2020 at 6:48:42 AM permalink
I know this one is very similar to the Cone Mountain puzzle, but that one was difficult to word. Hopefully this one will be more clear.

There is a teepee with radius 3 meters and height 5 meters. You wish to stake a rope to anywhere on the base of the teepee, wrap it entirely around the teepee once somehow, and tie the other end to the stake where you started.

1. What is the minimum length of rope needed?
2. Assuming the minimum length is used, what is the closest the rope gets to the tip of the teepee?


Photo credit: Wikipedia

  1. Please don't just plop a URL to a solution elsewhere until a winner here has been declared.
  2. All those who have won a beer previously are asked to not post answers or solutions for 24 after this posting. Past winners who must chime in early, may PM me.
  3. Beer to the first satisfactory answer and solution, subject to rule 2.
  4. Please put answers and solutions in spoiler tags.
Last edited by: Wizard on Mar 17, 2020
It's not whether you win or lose; it's whether or not you had a good bet.
ssho88
ssho88
Joined: Oct 16, 2011
  • Threads: 47
  • Posts: 552
March 16th, 2020 at 8:46:47 AM permalink
If slant height = 5m, minimum length of rope needed= (50*(1- cos(216 degree)))^0.5 = 9.5106m, minimum distance between rope and the tip = 0.5 * (100-50*(1- cos(216 degree))^0.5 = 1.5451m
Last edited by: ssho88 on Mar 16, 2020
Johnzimbo
Johnzimbo
Joined: Sep 29, 2010
  • Threads: 4
  • Posts: 958
Thanks for this post from:
Joeman
March 16th, 2020 at 10:17:44 AM permalink
I have been hoarding teepees.

Sorry, wrong thread
Wizard
Administrator
Wizard
Joined: Oct 14, 2009
  • Threads: 1390
  • Posts: 23442
March 16th, 2020 at 10:32:49 AM permalink
Five meters is NOT the slant height, it's the height from the center of the base to the tip.

I redid the numbers to not need to mention the slant height, fearing many people may not know what that is.
It's not whether you win or lose; it's whether or not you had a good bet.
DJTeddyBear
DJTeddyBear
Joined: Nov 2, 2009
  • Threads: 190
  • Posts: 10517
March 16th, 2020 at 11:08:57 AM permalink
Either the answer is 6pi or you mean the rope wraps up the teepee, reaching the peak, then drops to the starting point.

In that case, wouldn't we need to know the thickness of the rope?
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
Wizard
Administrator
Wizard
Joined: Oct 14, 2009
  • Threads: 1390
  • Posts: 23442
March 16th, 2020 at 12:22:56 PM permalink
Quote: DJTeddyBear

Either the answer is 6pi or you mean the rope wraps up the teepee, reaching the peak, then drops to the starting point.



There is a better answer in between those two extremes.

Quote:

In that case, wouldn't we need to know the thickness of the rope?



Just assume it's string. We don't need to muddy the water with rope thickness.
Last edited by: Wizard on Mar 31, 2020
It's not whether you win or lose; it's whether or not you had a good bet.
ssho88
ssho88
Joined: Oct 16, 2011
  • Threads: 47
  • Posts: 552
March 16th, 2020 at 4:06:36 PM permalink
Minimum length of rope = 11.6498m and it is 0.26545m away from the tip. I think DJTeddyBear should be the winner !

By the way, I think the teepee is stable and can withstand strong wind.

Last edited by: ssho88 on Mar 16, 2020
DJTeddyBear
DJTeddyBear
Joined: Nov 2, 2009
  • Threads: 190
  • Posts: 10517
March 16th, 2020 at 4:50:03 PM permalink
Quote: Wizard

Just assuming it's string. We don't need to muddy the water with rope thickness.

Whoa....

I just did a quick Google search for 喪ope. The first two links were images of rope for sale. It came in size from 1/4 to 1.

A similar Google search for 壮tring and also had links to purchase it, but only one of them had a size. 1/8.

Obviously a 1/8 string is gonna take 8 times the length to get the same lateral height as a 1 rope.

So my answer remains that there痴 insufficient information.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
Wizard
Administrator
Wizard
Joined: Oct 14, 2009
  • Threads: 1390
  • Posts: 23442
March 16th, 2020 at 7:48:49 PM permalink
Quote: ssho88

Minimum length of rope = 11.6498m and it is 0.26545m away from the tip. I think DJTeddyBear should be the winner !

By the way, I think the teepee is stable and can withstand strong wind.



Congratulations! This is the correct answer. I put the dimensions of the teepee incorrectly, but your answer is right for what I asked.
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard
Administrator
Wizard
Joined: Oct 14, 2009
  • Threads: 1390
  • Posts: 23442
March 16th, 2020 at 8:13:26 PM permalink
I hate to belabor this problem, but what would the answers be if the radius of the teepee were 5 meters and the slant height (distance from edge of base to tip) was 20 meters?
It's not whether you win or lose; it's whether or not you had a good bet.

  • Jump to: