Solve This Puzzle *RESOLVED*

**agmorgan** · Sep 24th, 2003, 10:33 AM

I thought I could write an algorithm to solve this, but it turned out
to be much harder than I expected!
There is a guy that works with me that worked on the Colossus at Bletchley Park
during WWII and he likes to come up with these things during tea breaks.

A man is on the outside of a circular pond and another man is in
a boat in the centre of the pond. What is the minimum speed that
the boat can travel at (relative to the mans speed) so that it
reaches the edge of the pond before the man does.

Note: the boat can change direction if it wants to!

**JPicasso** · Sep 24th, 2003, 11:17 AM

The first man is already on the edge, so there is no answer.

please post a pic. The starting and ending points are vague.

p.s. this should really be in the math section.

**agmorgan** · Sep 24th, 2003, 12:02 PM

The man is on the edge and he is running round the outside to get to the
point at which boat is going to hit land.
The guy rowing the boat is lazy and wants to go as slow as possible.
He doesn't want the first man to catch him though, cause hes been
sleeping with the first mans wife

Remember there is the possibility that the boat might change direction part way through.
This make sense now?

**Shaggy Hiker** · Sep 24th, 2003, 01:00 PM

That appears fairly easy, since the person will travel half the circumfrance (how do you spell that) of the circle (pi*R) while the boat must travel only R. Therefore, shouldn't the boat have to travel at (1/pi) * the speed of the walker?

**JPicasso** · Sep 24th, 2003, 03:11 PM

Shags, yes, but he can travel slower if he constantly adjusts his course... that is,
when smiley is at 9oclock, the boat should be traveling towards 3oclock, and when smiley is at 6oclock, the boat should travel towards 12 oclock.

This would result in a spiral out pattern, of which, I have no idea how to solve, well, I have an idea, but not the energy. especially since he shouldn't be sleeping with anyone's wife! I hope he gets caught.

[edit]
Problem with this is that the slowest he could travel would be 0 (fav vel units here) and just circle around and around till the other poor ******* dies of a heart attack.
Must be some other limitation here...
[/edit]

**Shaggy Hiker** · Sep 24th, 2003, 03:49 PM

I always mis-read the problem the first time. I thought there was a fixed goal, but there clearly isn't, I just mis-read it. This sounds much like a problem I had in my second semester of calculus. I don't remember the solution, only that there was a spiral. Furthermore, I don't remember much of anything else about the class.

On the other hand, I would like to comment about those two lunatics. The guy in the boat would be better off taking a nap and letting the wind do the work, while the guy on the shore ought to get a clue! I can just imagine him running in frantic circles like some yappy little doglet thing hoping to actually encounter the boat. He should take a nap instead. Once they are both asleep, the problem will be much simpler, since nobody will care.

**jemidiah** · Sep 24th, 2003, 06:12 PM

Well, as JPicasso said, he could just go 0 and keep turning if the point is the opposite point of the man. Otherwise, he can go (1/pi+1/infinity)*(speed of guy walking) units (about like shaggy said).

btw. the 1/infinity is there so he beats him by the smallest margin possible instead of arriving there at the exact same time.

**DiGiTaIErRoR** · Sep 25th, 2003, 02:03 PM

Originally posted by jemidiah
Well, as JPicasso said, he could just go 0 and keep turning if the point is the opposite point of the man. Otherwise, he can go (1/pi+1/infinity)*(speed of guy walking) units (about like shaggy said).

btw. the 1/infinity is there so he beats him by the smallest margin possible instead of arriving there at the exact same time.

Anything divided by infinity(except infinity) is zero.

**jemidiah** · Sep 25th, 2003, 07:01 PM

As I have been taught, it's infinitely small, which may as well be zero. But, to avoid an argument, I'll just say 1/pi+(a very, very small number)

**agmorgan** · Sep 26th, 2003, 08:16 AM

Originally posted by jemidiah
Well, as JPicasso said, he could just go 0 and keep turning if the point is the opposite point of the man. Otherwise, he can go (1/pi+1/infinity)*(speed of guy walking) units (about like shaggy said).

btw. the 1/infinity is there so he beats him by the smallest margin possible instead of arriving there at the exact same time.

Apparently not.
Seems it was actually another puzzle written out differently.
http://rec-puzzles.org/new/sol.pl/geometry/duck.and.fox

It looks like JPicasso was on the right track; and the answer is
1/4.6 if you cant be bothered to follow the link

**JPicasso** · Sep 26th, 2003, 08:23 AM

it didn't make sense to try and calculate the boats speed, since, if he had brought some sausages, he could have out stayed the man on shore.

It makes more sense to try and calculate the man on shore's speed to catch this dude. (assuming constant speed)

**trasogus** · Oct 13th, 2003, 02:15 AM

Well, my dear friends, lets assume that the boat never changes the direction, even so, I have noticed some mistakes in solutions....If and only If the problem goes with fixed direction of movement, then the sollution will be Y > X/sqrt(pi) where Y is speed of boat and X is speed of this poor guy. And this means that Y should be greater than X/sqrt(pi) by infintly small positive number (which is in some cases is actually 0, as was mentioned above, but for the sake of the problem 0 can be excluded)

I'm not so good yet with trigonometric functions, so i wouldn't comment on actual sollusion.

P.S.

I'm sure that you'll find lots of mistakes in my grammar and spelling

Thread: Solve This Puzzle RESOLVED

Thread Tools

Display