A Riddle About A Bear

[elfan]

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?

"If I asked you whether you guard the heaven, will you say 'yes'?"

If the answer is "yes" then he guards the heaven, if the answer is "no" then he guards the hel_l.

[Soju]

"If I asked you whether you guard the heaven, will you say 'yes'?"

If the answer is "yes" then he guards the heaven, if the answer is "no" then he guards the hel_l.

Yes, that is a good solution and doesn't require the guard to have any knowledge about the other guard. For that matter, your solution doesn't require the guard to even have any knowledge that there is even another guard or door. Both your solution and Thatguy's though are asking a question about a question. Now what if you changed the puzzle to state that your single question could not mention any other question. Can you still solve it? There is yet another solution for this case, which also does not require the guard to have knowledge of the other guard's truthfulness.

[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

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, thank you for your, as always, insightful response. As for the practical limitations, (when the "walking circles" are becoming very small), of the puzzle solutions I fully agree with you. However, what I was trying to say in my "appendix" above to which you responded, was that the fact that some part of the walking person is extending over the exact point of the pole doesn't necessarily mean that a part of the person will not be travelling west (disclaimer: see below).

Let me illustrate what I mean with an example:

Let's say that the person stretches out his left arm, "gripping" the Earth's axis (the imagined axis around which the Earth revolves) coming out of the exact point of the South Pole. He then walks in a circle around the pole while "holding on" to this axis. Nothing strange so far, I hope .

Now, let's say the person moves 15 cm closer to the axis/pole, still holding out his left arm. Now the infinitesimally thin axis will penetrate his arm somewhere around his left wrist, and his left hand will be on the other side of the axis/pole. He starts walking in a circle again, "locked" by the axis through his wrist. As stated in my previous post, his whole body (except for the infinitesimally small part that the axis occupies, which will be standing still) will still move counterclockwise/west around the axis (even his left hand, which is located on the other side of the pole). We can take this scenario a step further and let larger chunks of the person's body extend over the pole, but, as you Soju have correctly pointed out, we would very quickly run into practical problems (e g is the person really still "walking"?; is the person really still going in a circle?).

Ok, I was only trying to elaborate on this from a more theoretical viewpoint, and maybe I have to practise my "explaining skills" in English a bit more (obviously, English is not my native language).

Regards

[Soju]

Chemist, I now understand what you're talking about, and agree with your assessment if the person was being wheeled around rather than walking. My point has to do with the actual activity of walking, whereby the actual left foot is extending over the axis and forward motion of the left foot is necessary in order to fulfill the definition of walking. If the left foot never takes a step then I fully agree with your analysis. One's hand, arm, or other parts of their body are technically able to avoid any eastward movement, but the left foot is not. Of course, as stated in an earlier post, this only comes into play once the circle around the axis is so small that the left foot can no longer avoid stepping over the axis. If I'm still missing something or if you disagree, please explain why.

P.S. Being you stated that English isn't your native language, I'm impressed at your excellent mastering of it.

Edited July 23, 2007 by Soju

[chemist]

Chemist, I now understand what you're talking about, and agree with your assessment if the person was being wheeled around rather than walking. My point has to do with the actual activity of walking, whereby the actual left foot is extending over the axis and forward motion of the left foot is necessary in order to fulfill the definition of walking. If the left foot never takes a step then I fully agree with your analysis. One's hand, arm, or other parts of their body are technically able to avoid any eastward movement, but the left foot is not. Of course, as stated in an earlier post, this only comes into play once the circle around the axis is so small that the left foot can no longer avoid stepping over the axis. If I'm still missing something or if you disagree, please explain why.

P.S. Being you stated that English isn't your native language, I'm impressed at your excellent mastering of it.

Again, thanks for your reply. I actually believe that we are in full agreement regarding this puzzle. As for my recent reasoning, the sentence above in bold (the "bolding" was done by me) is a key statement, and that is why I used an example where the person had his arm extended over the pole (in this example I also assumed that the person could still walk in a perfect circle (without having to put his left foot over the axis, naturally) despite the fact that the circle is rather small).

Finally, I would like to thank you for your kind words about my English skills.

Regards

[Humphrey Bear]

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

Sorry - I was there a couple of weeks ago. It's all this global warming, you see.

[Mid]

negative , negative .............

[elfan]

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've found a more interesting puzzle similar to this here: http://xkcd.com/246/