[itachi-san]

You are standing at the center of a circular field. The field has a low wire fence around it. Attached to the fence is a large, hungry, deadly Pit Bull. Assume for this puzzle, that the dog can only run exactly at the perimeter of the field. The dog can run four times as fast as you can. How can you get off the field without the Pit Bull tearing you to shreds?

[bonanova]

Let's say your best chance is to run directly away from the dog and get out of the circle before he gets to your exit point.

That won't work - your distance is R - the circle's radius, and the dog's distance is PIxR.

Since PI < 4, he's gonna getcha.

A better strategy will be to run in a quickly expanding spiral - to your left or right, away from the dog.

I'm betting that would work, but I don't have the math, yet, to prove it.

Just need a formula for the length of a spiral of a given angle - should be around the web somewhere.

[Guest]

I think i got this one.

Go to center of field and then run towards the fence exactly opposite to the dog. Run for just slightly less then R/4. Let say you are at point X. In the meantime the dog will run clockwise or anti-clockwise. After reaching X run in the direction in which dog ran. Now you are completing the circles faster than dog so you can reach a point where the centre of the circle, you and dog are in a straight line. Then simply run towards the fence.

[itachi-san]

I think i got this one.

Go to center of field and then run towards the fence exactly opposite to the dog. Run for just slightly less then R/4. Let say you are at point X. In the meantime the dog will run clockwise or anti-clockwise. After reaching X run in the direction in which dog ran. Now you are completing the circles faster than dog so you can reach a point where the centre of the circle, you and dog are in a straight line. Then simply run towards the fence.

You have part of the answer, but there is more to it. Good work though.

[Guest]

You have part of the answer, but there is more to it. Good work though.

There is one more thing that I figured out.

The radius should be less than R/4 as well as greater than (4-pi)R/4. Otherwise going to the fence means dog can catch you.

[bonanova]

Can't find a good spiral length formula, but I don't think it's needed.

[1] Begin by running radially away from the dog.

[2] The dog will chase you, either to the left or to the right.

[3] Continuously adjust the angle you run, to keep him directly behind you.

[4] You can buy enough distance this way to escape.

At small radii, a spiral path can keep the dog directly behind you long enough

to outrun him when you no longer can.

Just intuition - no math.

[Guest]

You are standing at the center of a circular field. The field has a low wire fence around it. Attached to the fence is a large, hungry, deadly Pit Bull. Assume for this puzzle, that the dog can only run exactly at the perimeter of the field. The dog can run four times as fast as you can. How can you get off the field without the Pit Bull tearing you to shreds?

When you reach the centre the dog is still at the edge and you have enough speed to run the readius faster than the dog can run half of circumference - assuming you run opposite direction, unless you take the dog on or want to try jumping over it!

So r is < than cirumference... also assume that dog is free to travel full circle and that attached (L) is not greater than the difference of 1/2 circumfrence - r

I have been bitten by a dog when I was 14 uptill then I was doctor doolittle - and at 18 was chased by a dog that was normally tethered, I out climbed it, 5m up a stack of timbe/lumber (just a bit higher than a pole in a lake). I can for the life of me rember actually climbing it, I needed a ladder to get down and it was not the safest stack to climb, well considering the options it propbably was as good as any,

Edited April 16, 2008 by Lost in space

[bonanova]

OK forget the spiral thing.

You can run circumferentially as fast as the dog can so long as he's at R and you're within R/4.

If the dog is behind you at that point, your distance is 3R/4 and the dog's is PIxR.

The arrival time ratio now is PI/3 >1.

It takes the dog longer.

You're out.

[itachi-san]

There is one more thing that I figured out.

The radius should be less than R/4 as well as greater than (4-pi)R/4. Otherwise going to the fence means dog can catch you.

Excellent job!

Yes, there are 2 requirements.

1st, you must be closer to the dog than the center = (4-pi)R/4 which is roughly .215R.

2nd, you must be far enough away so that you can escape him by running in the opposite direction = R/4 or .25R

So, in order to escape you must run in a circle at a radius between these 2 points and then when the dog is opposite you, head for the hills!

The small radius looks like: .215R<Distance from center<.25R

[Guest]

Who knew that this forum would be so informative. You guys are saving lives here.

[akaslickster]

Who knew that this forum would be so informative. You guys are saving lives here. didn't have to bother the Red Cross for a helicopter.