A Riddle About A Bear

[chemist]

Yes, about a bear, not about a beer. Sorry about that .

Anyway, a bear walks 20 km heading south. Then he walks 20 km to the west, and finally 20 km to the north, only to find that he has returned to the exact same point from which he started. What color is the bear?

If that one is too easy, I humbly apologize .

Regards

[kelvinj]

White?

[chemist]

White?

Most likely correct. A little bit too easy, right?

Regards

[kelvinj]

This is one of my favourites; A bloke dies and passes over to the other side where he finds himself confronted by two unmarked doors, one of the doors is the entrance to heaven, the other is the entrance to hel_l. There are two gaurds in front of the doors, one guard will allways tell the truth, the other guard will allways lie. The bloke is allowed just one question to establish which door leads to heaven, what does he ask?

[kelvinj]

I should have made it clear that he has no way of knowing which guard lies or which one tells the truth.

[Soju]

White?

Most likely correct. A little bit too easy, right?

Regards

That was pretty easy, but perhaps a little bit more challenging is can you name two places on earth where this condition would be possible to accomplish?

[Soju]

This is one of my favourites; A bloke dies and passes over to the other side where he finds himself confronted by two unmarked doors, one of the doors is the entrance to heaven, the other is the entrance to hel_l. There are two gaurds in front of the doors, one guard will allways tell the truth, the other guard will allways lie. The bloke is allowed just one question to establish which door leads to heaven, what does he ask?

I also like that puzzle a lot, but being I already answered it when it was first posted won't post the answer again and see if others can come up with a solution.

[kelvinj]

There is only one, there are no bears at the other end.

[Martin]

Nor can you walk south at the other end.

[chemist]

This is one of my favourites; A bloke dies and passes over to the other side where he finds himself confronted by two unmarked doors, one of the doors is the entrance to heaven, the other is the entrance to hel_l. There are two gaurds in front of the doors, one guard will allways tell the truth, the other guard will allways lie. The bloke is allowed just one question to establish which door leads to heaven, what does he ask?

I also like that puzzle a lot, but being I already answered it when it was first posted won't post the answer again and see if others can come up with a solution.

Hi there, you riddle-solvers !

I just returned from a short vacation from my computer, only to discover that this thread has evolved .

I too feel that I am disqualified from the puzzle above, as I have seen it (and its answer(s)) many times before. There ain't no fun in just writing down what you know without having to use your brain one bit in a case like this, I think. So I agree with Soju. Let some other candidates, who maybe haven't come across this puzzle before, have a go at it.

If no solutions start dropping in, well, then some of us might have to "sacrifice" ourselves .

Regards

PS Regarding the puzzle above: kelvinj, apart from the fact that the guy who wants to go to Heaven doesn't know who is lying and who is telling the truth (which you have already pointed out), shouldn't it also be mentioned that the guard who is telling the truth knows that the other guard is lying, and vice versa?

[chemist]

That was pretty easy, but perhaps a little bit more challenging is can you name two places on earth where this condition would be possible to accomplish?

I am not sure what you mean here. As kelvinj pointed out, there are no bears in Antarctica (but there are plenty of penguins ). Furthermore, Martin correctly indicated that there is nowhere to go but north when you are standing at the South Pole, which means that going south - west - north, starting at the South Pole, is impossible. So please give me some more details, and I will be more than happy to try to come up with an answer .

Regards

Edited July 20, 2007 by chemist

[Lickey]

Yes, about a bear, not about a beer. Sorry about that .

Anyway, a bear walks 20 km heading south. Then he walks 20 km to the west, and finally 20 km to the north, only to find that he has returned to the exact same point from which he started. What color is the bear?

If that one is too easy, I humbly apologize .

Regards

The bear is the same colour where ever he goes..

[Soju]

That was pretty easy, but perhaps a little bit more challenging is can you name two places on earth where this condition would be possible to accomplish?

I am not sure what you mean here. As kelvinj pointed out, there are no bears in Antarctica (but there are plenty of penguins ). Furthermore, Martin correctly indicated that there is nowhere to go but north when you are standing at the South Pole, which means that going south - west - north, starting at the South Pole, is impossible. So please give me some more details, and I will be more than happy to try to come up with an answer .

Regards

Ok, assume the bear (or human or any other animal if you wish), can travel anyplace on the earth. Name one other place on earth, other than the north pole, where some person or animal can walk 20 km south, then 20 km west, then 20 km north and end up at the exact same starting point. It is correct that you cannot start at the south pole because the only direction you can travel from the south pole is north. Think about it - there is a solution.

Edited July 21, 2007 by Soju

[Soju]

PS Regarding the puzzle above: kelvinj, apart from the fact that the guy who wants to go to Heaven doesn't know who is lying and who is telling the truth (which you have already pointed out), shouldn't it also be mentioned that the guard who is telling the truth knows that the other guard is lying, and vice versa?

Actually, that's not entirely true. But the guards do need to know that one door leads to heaven and the other to he11 and they need to know which of those two doors they're guarding. Even if they don't know if the other guard lies or tells the truth, there still is at least one possible solution. Of course you have to then make an assumption about what the guard's response will be to a question which they don't know the answer to. In this case, the one solution I'm thinking of would require the truthful guard to respond with "I don't know", or to perhaps remain silent if he didn't know the answer. Whereas if the untruthful guard didn't know the answer, he could also choose to remain silent or to respond with "I know", being he doesn't know and so that response is a lie. A bit of a hint there for someone trying to solve this puzzle.

So to summarize, there are at least two solutions to this puzzle. One of them requires the guards to know the truthfulness/untruthfulness of the other guard, and the other solution does not require that. For an additional challenge, see if you can come up with both solutions.

Edited July 21, 2007 by Soju

[chemist]

Ok, assume the bear (or human or any other animal if you wish), can travel anyplace on the earth. Name one other place on earth, other than the north pole, where some person or animal can walk 20 km south, then 20 km west, then 20 km north and end up at the exact same starting point. It is correct that you cannot start at the south pole because the only direction you can travel from the south pole is north. Think about it - there is a solution.

Hi again Soju, and thanks for your clarification!

Ok, I have been thinking about the above for a little while now, and I actually think I have a solution: The person starts walking 20 km (going south) from a point that is located along a latitude (lat 1) that lies 20 km north of another latitude (lat 2), which has a circumference of 20 km (this means that we are pretty close to the South Pole here). The person then starts walking west along lat 2, and after 20 km he of course ends up at the same point from which he started on lat 2. Finally, he walks 20 km to the north, and naturally finds himself to be at the same point from which he started on lat 1 (i e the "original" starting point).

Soju, I must say that you seem to be one smart individual ! I myself didn't think about this alternative solution to begin with.

Regards

Edited July 21, 2007 by chemist

[Soju]

Well done Chemist! And being that the earth is nearly flat when talking about such small distances, if we calculate those latitudes, lat2 should be close to 20km / (2 x pi) or about 3.18 km north of the south pole. Being the earth is curved, it will actually be slightly more than that, and lat1 will be at approximately 23.18 km north of the south pole.

Now, that you've solved that, we have one solution at the north pole, another solution at any point along lat1 which you've described. Is that all the solutions or is there any other(s). If there are any other(s) what are they?

[percy2]

Ok, assume the bear (or human or any other animal if you wish), can travel anyplace on the earth. Name one other place on earth, other than the north pole, where some person or animal can walk 20 km south, then 20 km west, then 20 km north and end up at the exact same starting point. It is correct that you cannot start at the south pole because the only direction you can travel from the south pole is north. Think about it - there is a solution.

Hi again Soju, and thanks for your clarification!

Ok, I have been thinking about the above for a little while now, and I actually think I have a solution: The person starts walking 20 km (going south) from a point that is located along a latitude (lat 1) that lies 20 km north of another latitude (lat 2), which has a circumference of 20 km (this means that we are pretty close to the South Pole here). The person then starts walking west along lat 2, and after 20 km he of course ends up at the same point from which he started on lat 2. Finally, he walks 20 km to the north, and naturally finds himself to be at the same point from which he started on lat 1 (i e the "original" starting point).

Soju, I must say that you seem to be one smart individual ! I myself didn't think about this alternative solution to begin with.

Regards

He cannot walk west can he?

Cheers

[Soju]

Ok, assume the bear (or human or any other animal if you wish), can travel anyplace on the earth. Name one other place on earth, other than the north pole, where some person or animal can walk 20 km south, then 20 km west, then 20 km north and end up at the exact same starting point. It is correct that you cannot start at the south pole because the only direction you can travel from the south pole is north. Think about it - there is a solution.

Hi again Soju, and thanks for your clarification!

Ok, I have been thinking about the above for a little while now, and I actually think I have a solution: The person starts walking 20 km (going south) from a point that is located along a latitude (lat 1) that lies 20 km north of another latitude (lat 2), which has a circumference of 20 km (this means that we are pretty close to the South Pole here). The person then starts walking west along lat 2, and after 20 km he of course ends up at the same point from which he started on lat 2. Finally, he walks 20 km to the north, and naturally finds himself to be at the same point from which he started on lat 1 (i e the "original" starting point).

Soju, I must say that you seem to be one smart individual ! I myself didn't think about this alternative solution to begin with.

Regards

He cannot walk west can he?

Cheers

Sure he can. From the starting point, approximately 23.18 km north of the south pole, he walks south 20 kms to a point approximately 3.18 km north of the south pole. From that point you can still walk in any direction, and he chooses to walk 20 km west, completely circumnavigating the globe at that latitude, then walks 20 kms north (along the exact same path he walked the original 20 kms south), to return to the exact starting point. He never actually reaches the exact south pole, where it would be true that you could not walk west, east, or south. The nearest he ever comes to the exact south pole is 3.18 km away.

Edited July 21, 2007 by Soju

[chemist]

Well done Chemist! And being that the earth is nearly flat when talking about such small distances, if we calculate those latitudes, lat2 should be close to 20km / (2 x pi) or about 3.18 km north of the south pole. Being the earth is curved, it will actually be slightly more than that, and lat1 will be at approximately 23.18 km north of the south pole.

Now, that you've solved that, we have one solution at the north pole, another solution at any point along lat1 which you've described. Is that all the solutions or is there any other(s). If there are any other(s) what are they?

Well, other solutions that I come to think of are actually spin-offs from my previous suggestion, where the person circumnavigated the Earth (or the South Pole, if you will) only once. What I am talking about here are solutions in which lat 2 has circumferences of 20/2 km, 20/3 km, 20/4 km, etc. In these cases the person will head west on lat 2 until he has circumnavigated the Earth 2, 3 and 4 times, respectively, still returning to the point on lat 2 from which he started. In each case lat 1 must be placed 20 km north of lat 2, naturally. This reasoning leads to the conclusion that there are an infinite number of solutions to the "bear riddle".

Ok, this is what I can think of right now. Perhaps you know of other solutions? If you do, please let me know so that I (or somebody else) can try to figure them out .

Best regards

[Soju]

Chemist, you came up with all the solutions that I could think of and think it is impossible to have any other solutions, assuming the earth was a perfect shaped globe and that the traveling is done on the surface of the earth.. Theoretically, if a infinitely small pinpoint is doing the traveling, then there are an infinite number of solutions as you say. In the real world though, the width of one's body would limit the number of solutions. For example, if one's body was 1 meter wide, then assuming one is traveling these paths with the center of their body being centered on the paths, as lat1 approaches 20km from the south pole, and lat2 approaches the south pole, the westerly trip becomes impossible once lat2 is less than 0.5 meters. This is because the left part of one's body would then extend over the south pole, meaning only part of the body was traveling west, while part of the body would be traveling east. Although it would depend on how you interpret the puzzle as to whether you should disallow such cases or not. But even if that is allowed there obviously comes a point where the differences in successive solutions becomes so minute that it would be impossible for any living being to distinguish them and walk them as separate paths/solutions. Of course each solution, other than the obvious one of starting at the north pole, are actually a circle of latitude composed of an infinite number of points, so each of these solutions contains an infinite number of starting points.

[chemist]

Soju, I agree with you. I too think that it will not be possible to find any more solutions to the problem.

As for the practical aspect, you are of course right. Finally, when it comes to the last sentence in your post: "Of course each solution, other than the obvious one of starting at the north pole, are actually a circle of latitude composed of an infinite number of points, so each of these solutions contains an infinite number of starting points.", I couldn't have said it better myself . Actually, I thought about adding something similar when I wrote about the additional solutions to the puzzle yesterday.

Soju, I would like to thank you for contributing to this thread, as I think that your posts and input have made "the bear riddle" a lot more interesting than it was in the first place .

Regards

[chemist]

Actually, when it comes to the practical limitations of the additional solutions mentioned in the posts above, I think I might have to change my mind a bit. When the person is very close to the South Pole, and a part of his body is extending over the pole, wouldn't it be correct to say that also the part of the body that is on the other side of the pole is travelling west, since the whole person would virtually be "spinning" counterclockwise around an imagined axis emanating from the pole? (However, a "part" of the body, through which this imagined axis is erupting, would of course be standing still. This "part" would be infinitesimally small, though.)

Regards

[Kalavo]

Actually, when it comes to the practical limitations of the additional solutions mentioned in the posts above, I think I might have to change my mind a bit. When the person is very close to the South Pole, and a part of his body is extending over the pole, wouldn't it be correct to say that also the part of the body that is on the other side of the pole is travelling west, since the whole person would virtually be "spinning" counterclockwise around an imagined axis emanating from the pole? (However, a "part" of the body, through which this imagined axis is erupting, would of course be standing still. This "part" would be infinitesimally small, though.)

Regards

No, the directions North, South, East and West are relative to the planet, not relative to your position in space. So if you are standing still on one of the poles, you are standing still, you are not heading N/S/E/W, but you are rotating and revolving around the Sun.

[Lickey]

I thought the question was what colour is the bear! and the answer is, The same colour as when he started his journey!

[thatguy]

assuming both guards have total knowledge, ask one guard: "will the other guard tell me he's guarding heaven?" the truth will be the opposite of the answer given.

That is, if he says no, the other door is heaven, if yes, it isn't.

[chemist]

Actually, when it comes to the practical limitations of the additional solutions mentioned in the posts above, I think I might have to change my mind a bit. When the person is very close to the South Pole, and a part of his body is extending over the pole, wouldn't it be correct to say that also the part of the body that is on the other side of the pole is travelling west, since the whole person would virtually be "spinning" counterclockwise around an imagined axis emanating from the pole? (However, a "part" of the body, through which this imagined axis is erupting, would of course be standing still. This "part" would be infinitesimally small, though.)

Regards

No, the directions North, South, East and West are relative to the planet, not relative to your position in space. So if you are standing still on one of the poles, you are standing still, you are not heading N/S/E/W, but you are rotating and revolving around the Sun.

Well, this thread just keeps on giving .

Kalavo, I seriously believe that you misunderstood what I wrote. In discussing solutions to "the bear riddle" we have so far only talked about movements relative to the Earth. The Earth's rotation and its movement around the sun are totally irrelevant factors in the discussions on this thread. I assume that you have read all the previous posts regarding the problem at hand?

Anyway, when I talked about the person "spinning" around the South Pole, I naturally referred to a scenario when the person is walking in very small circles around the exact point of the pole (i e the person is moving relative to the Earth).

I of course realize that a misunderstanding like this can occur if one only reads the post you quoted above, so maybe I (in the post you are referring to) could have explained more clearly what I was getting at .

Regards

Edited July 22, 2007 by chemist

[chemist]

I thought the question was what colour is the bear! and the answer is, The same colour as when he started his journey!

Are you sure about that? Maybe the bear was a seriously disturbed animal, who decided to roll around in its own shi_t during the journey. Well, who knows?

Regards

[Soju]

Actually, when it comes to the practical limitations of the additional solutions mentioned in the posts above, I think I might have to change my mind a bit. When the person is very close to the South Pole, and a part of his body is extending over the pole, wouldn't it be correct to say that also the part of the body that is on the other side of the pole is travelling west, since the whole person would virtually be "spinning" counterclockwise around an imagined axis emanating from the pole? (However, a "part" of the body, through which this imagined axis is erupting, would of course be standing still. This "part" would be infinitesimally small, though.)

Regards

I'm not quite sure if I fully understand what you're getting out. Are you talking about a person with their left foot on the south pole and pivoting about on that foot while the right foot is taking the steps? I briefly thought of that case but discounted it due to the fact that such doesn't match my definition of 'walking'. If you do allow this case to fall under the definition of walking, then if the pivot point is exactly at the south pole, and the pivoting of the entire body was about that axis, then you would only have westward (counter-clockwise) movement. But if the pivot point wasn't exactly aligned with the south pole, then you'd have eastward, as well as northward, etc. movement in part of the body. If you think about the area of the bottom of the foot between the pivot axis and the south pole axis, this is easy to visualize.

If the animal/person is actually walking, then the way one typically walks, when walking in a circle, would be to take one step, pivot the foot an appropriate number of degrees, take the next step, pivot the foot, etc. Or else to move the feet/legs off at an angle rather than straight on. So typically a person would walk a circle as a series of straight line segments, so not actually a true circle. Even if you tried to curve your step as it was being made, still you couldn't do so in a perfect manner. It would just be a series of smaller straight line movements along with frequent adjustments. It is physically impossible to walk an absolutely perfect circle.as that would require an infinite number of precise angular adjustments to the direction of the walking.

So looking at it precisely, I say that part of the body would be walking eastward (or at least in a non-westerly direction), while the major part is walking in a westward direction. Now the argument could be made that westward walking anyplace on the earth does involve some eastward motion, such as the swinging of one's arms, on the backward stroke is eastward movement, even when the person is walking westward. Or that the entire body makes some forward/backward rocking movements. Yet I don't think anyone would argue that those factors affect the definition of walking westward. But when one's foot starts passing over the south pole, then I think it would be hard to get any sort of consensus about if the person is truly walking westward or not. So maybe it's best to say that there are a finite number of unequivocally possible solutions in the real world, above which there are additional finite number of solutions depending upon how you define westward walking, followed by an infinite number of solutions but which are physically impossible to achieve due to the limited ability of a human or animal to distinguish very minute distances and to be able to walk such paths as distinct paths.

Anyways, a good puzzle, Chemist. Hope to see more here and to be able to discuss them with someone as yourself that likes to go into the details of what makes them tick.

[Soju]

I thought the question was what colour is the bear! and the answer is, The same colour as when he started his journey!

Lickey, I'd give you partial credit for your answer! Clearly not what was intended but yet a clever way of answering the riddle. But if you transported a black (or brown) bear to the north pole, or Antarctica, and had it walk for 60 km, it would probably end up being more white than black or brown, due to a large accumulation of ice and snow on it's fur. So it wouldn't be the same color anymore if looking at it like that. And then 'white' would be a good answer regardless of what kind of a bear it was.

[Soju]

assuming both guards have total knowledge, ask one guard: "will the other guard tell me he's guarding heaven?" the truth will be the opposite of the answer given.

That is, if he says no, the other door is heaven, if yes, it isn't.

Good job, Thatguy. Your solution is correct. Now can you or anyone else come up with an alternate solution that doesn't require either of the guards to have any knowledge of the opposite guard's truthfulness/untruthfulness?