[Guest]

Okay, my first post here, usually I'm just a lurker, so I thought I'd start with a new puzzle(which I didn't see when I searched )

You are passing the time rowing about in your canoe, in the middle of a lake that makes a perfect circle. You are about to head back to shore when you notice a very hungry ogre looking at you from the shore. After rowing a bit while watching him, you notice a few things:

- The ogre runs 4 times faster than you can row.

- You can run twice as fast as the ogre (on land, you can't run on water...)

- The distance from the center of the lake to the shore is 1 mile (i.e, the radius of the circle)

How do you escape the hungry ogre? Here's your hint:

Circumference = pi*diamater

The area of the circle isn't important to the puzzle.

[bonanova]

This has been posted and solved at least twice, in different settings, and

Searching for the previous posts is difficult owing to different settings for the puzzle.

There are two solutions of interest - the one that gets the person to safety the quickest,

and the one that keeps the greatest distance between the person and the danger.

I posted the second solution, previously, but I can't find the reference.

If anyone's interested, I can reproduce it.

- bn

is the solution for quickest escape [already given in this thread by darmelpitts,

Tuckleton and Hugo], and also the solution for the greatest distance escape. The second

solution permits escape from a faster opponent - one that is 4.6 times faster than you.

[Guest]

Remember, Ogres are stupid. If you row ABSOLUTELY ONE HUNDRED PERCENT AWAY FROM HIM, and the line you are rowing passes through the center of the circle (I think thats called a chord? then again chords hit bot sides, so nvm), he won't know whether to go around the left to kill you, or go around the right to kill you. With his brain working this hard, he will likely have some sort of stroke, and then he'll be worried about that, and not you.

[Guest]

[/spoiler=Answer... I Think ]........ ................................. ............ .......... .......... opposite the Ogre(what on earth is an Ogre?), ........................ ..................................................................................

This is an ogre:

[bonanova]

Can you escape an even faster ogre if you paddle in a spiral?

When your escape path is a tangent to the maximum circle that aligns you, the ogre and the center of the lake, you and the ogre will arrive simultaneously at the shore point if the ogre's speed is 4.6 times yours.

See the red paths in the diagram, drawn for R/r = 4.6, which is also the length ratio of the circular and straight paths.

Suppose you attempt to increase your angular separation from the ogre by following the black [approximate] spiral path which changes course by 45^o at the points shown. This path was chosen for ease of computing your arrival time at the shore. How far can the ogre travel in that time?

It turns out you will fare much worse. The ogre now has enough time for 1.5 full circles of the lake! Of course he won't go that far; he'll just wait on shore for supper to arrive.

The tangent is the optimal escape path.

It permits survival from a predator that has 4.6 times the victim's speed.