mersenneforum.org  

Go Back   mersenneforum.org > Fun Stuff > Puzzles

Reply
 
Thread Tools
Old 2003-09-05, 06:06   #1
Fusion_power
 
Fusion_power's Avatar
 
Aug 2003
Snicker, AL

7×137 Posts
Default Goat grazing inside a circular fence.

This is a similar problem to the one about the cow grazing beside the silo.

There is a goat that is inside a circular fence. But because the goat is always jumping the fence and visiting distant but lush pastures, the owner decided to tie him inside the pen so he can't leave. The fence is 100 ft in diameter The goats tether is exactly 60 feet long and is attached to a fence post. Presume the goats head is at the end of the tether for purposes of solving this equation. The tether is just enough of a nuisance that the goat does not jump the fence.

If the goat eats all the grass it can reach on the first day and the owner then ties him to a fence post exactly opposite (across the circle from) the one he was previously tied to, how much of the grass (area) will the goat be unable to graze over the two days?

Fusion
Fusion_power is offline   Reply With Quote
Old 2003-09-23, 23:04   #2
dweick
 
Apr 2003

2×5 Posts
Default

I decided to solve it using software approximation.

Visualize a 100' radius circle within a box 100' on a side. Make the upper left hand corner of the square (0,0). The center of the grassy area is at (50,50). You have one goat rope tethered at (0,50) and a second tethered at (100,50).

For every point on the 100x100 grid compute the distance between the point at the three targets (above). If the distance is less than 50' to the center target and the distance to each goat tether point is greater than 60' then add 1 sq ft to an accumulator.

To make the software converge better I used a dx and dy to further divide the grid. Using 0.001 for dx and dy (so I'm determining whether each 0.00001 sq ft patch in the 100x100 grid is an area of interest I came up with 442.7485 sq ft. I'll round that off to 442.75 as my answer.

Takes 30 secs or so on my 700MHz PIII laptop to make a run at the above resolution. If I use 0.1ft dx, dy I get 442.59 sq ft.
dweick is offline   Reply With Quote
Old 2003-09-25, 04:40   #3
Fusion_power
 
Fusion_power's Avatar
 
Aug 2003
Snicker, AL

7×137 Posts
Default

Interesting solution.

The entire circle has an area of:
3.14 * 50 * 50 = 7850 square feet.

If the goat can't reach 443 square feet, then 7850 - 443 = 7407 square feet that the goat can graze.

Somewhere around here I have a pi calculator based on a similar principle to the method you used.

Fusion
Fusion_power is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
The Truth is Inside there :)): a1call Lounge 9 2018-02-28 10:45
The Secret CPU Inside Your Intel Processor ewmayer Tales From the Crypt(o) 21 2017-11-23 03:02
Fireworks from the inside Mark Rose Lounge 1 2014-07-07 23:37
The prime or the goat? only_human Puzzles 6 2003-12-19 02:02
Does Prime95 has a list of primes inside it??? hyh1048576 Software 5 2003-08-20 13:38

All times are UTC. The time now is 08:08.

Fri Mar 5 08:08:54 UTC 2021 up 92 days, 4:20, 0 users, load averages: 1.20, 1.39, 1.37

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.