Sunday, September 16, 2007

Solutions Often Bring New Problems.....

.......as we scientists know. It often happens, solve one problem, and a whole plethora of new ones rear their ugly collective head in protest.

I am about to prove that this not only happens in Physics, it happens in blogs as well.

Recall that strange picture I posted on August 15th, entitled

Not a Math Riddle for a Change......

If not, have a look at it. Only five comments, though.

Here is the same image followed by two subsequent others:




The first image is the original puzzle. The second a fraction of a second later, and the third, later still.



When I say 'later' I mean about '1/10,000,000' th of a second.

It is of course, a nuclear bomb, photographed very soon after detonation.

Not in Nevada, but New Mexico. In fact, it is Trinity. The curious shapes seen are a feature of the vaporisation of the tower it was on, visible in photo 1. It was so hot, the sand was turned to glass, and the Indians sell the pieces for $1 each. I have one myself!

Well, that is the solution.

For that, there is a price, as promised. More new problems, as here the students have just started returning to the University.

How many can you answer? Just five for perusal, and for you all to comment upon.

1) You have two coins in your pocket that add up to 26 cents. One of them is not a quarter. What are the coins? (easy)

2) A cylindrical hole 6 inches long is drilled straight through the center of a solid sphere. What is the volume remaining in the sphere? (hard)

3) Three rabbits are crossing the road, a busy road. A father rabbit, a mother rabbit, and a baby rabbit. Suddenly the strong father rabbit sees a chance, takes up baby in his arm, and drags the mother rabbit by the other hand across the road. They arrive there without injury. The baby rabbit then says "Thank you daddy, for getting all two of us across the road safely" Please explain. (medium)

4) You have three cards, (two aces and a queen), all face down. You are asked to find the queen, and you are asked to pick one card only. Then , the magician looks at them all, and promptly turns face up , an ace. What is the probability that your card is the queen? (hard)

5) A snail falls into a well which is 20 meters deep. He starts to climb up immediately, and in the daytime, he goes three meters up, but at night falls two meters back again. Assuming he starts the ascent at dawn on the first day, how many days is it before he emerges? (easy)

Blame it on the freshers, who never do any work in the first week anyway.

Isn't this lovely?

As of 26 September, no-one here has even got three out of five correct yet, and you all must be punished by a sixth, since no-one has remembered my birthday (Hey - look it up, I know you are smart-ish).

This one is insuperably difficult, and if anyone gets THIS correct, and I am satisfied that the answer is original, AND you understand it, then the reward shall be a gift from you to me and I will forget that you forgot.

6) What is the difference between left and right?

So certain am I? So certain I am.

32 comments:

AkiToo said...

1 out of three ain't bad, Mr Clio.

Wyman Stewart said...

1. Surely if one of them is not a quarter, then the other one is.

2. I refrain from this pain, since I see someone has answered the question. Clio, I think you and I will not be invited to join Mensa. Well, I won't. You were clever enough, there is still hope for you. Good luck.

3. The key here seems to be "all two of us". In baby rabbit's parlance "all two" implies: baby in daddy's arm is one set of two and daddy dragging mother is another set of two, therefore all is inclusive of both sets, there being two sets. There can be little doubt baby rabbit is the reincarnation of Gauss to be so wise at such a tender age.

4. The probability that your card is the queen is 1 in 2.

5. I say he emerges on the 21st. day. However, it depends on how you define emerge.

Best of luck to all others, whose answers shall enlighten me.

AkiToo said...

Wyman, you get one out of the five!

It's getting hotter!

Wyman Stewart said...

:-( You mean it rained and the poor snail drowned? Afterall, this question is not a case of Zeno's Paradox.

Ouch!!! My snailbrain just saw the light at the end of this tunnel/well. Although I may be right that how you define emerge is important, I have drowned in my self-perceived brilliance. Pass the Dunce hat, please. Thank you.

AMIT ROY said...

A few answers: (I dont think you have posted it yet...)

1) 25 cents and 1 cent (one of them is not a quarter, the other one is).
2) 4/3 *pi* R^2 minus pi * r ^2 * 6
3) Confusing? Need help unerstanding this..
4) 0.5 (given that we know first is ace, the probablity of queen out of two cards where one is queen is 1/2)
5) 18 days (on 18th day the snail starts journey from 17th meter and does 3 meters, why should he fall back again).

AkiToo said...

Hi Amit,

Two out of five ain't bad either.

Pity they are not the same ones as Clio or Wyman.

Come on guys, there must be half a brain between you!

He He He!

AkiToo said...

Was that you Wyman? It was so out of character it must have been your brother I think. I thought you knew me better than to put insults here.

If it WAS you Wyman, you did not notice the "!" after the words "brain between you". The phrase is a kindly way of making people think in the English vernacular.

Wyman Stewart said...

It was me. Have e-mailed you. Delete me.

AkiToo said...

Yes, David, you would!

Wyman Stewart said...

6) I will venture the difference between left and right is zero. Or the difference between North and South. Or I have added to my list of wrong answers, therefore increasing the probability that I should take up studying Logic in my spare time.

Happy Birthday!!! Is this wrong too? I was going to ask your birthdate, since I did not recall seeing it anywhere. I hope it could not be deduced through the reading of one of your blogs or comments. Logic questions have me questioning everything after a short time. Again, Happy Birthday!!!

Unknown said...

lets see.........

Unknown said...

ok - number 1 - a quarter and a cent / penny (reasons already given)

2 - cant answer as I havent a clue as we dont know how wide the drill is.....it might be 1/4", might be almost 6 inches......?

3 - ALL two off us? sounds like kids logic to me - because daddy couldnt have got them across the road without being there himself...

4- easy. the chance if the dealer taking an ace is 2/3 so therefore the chance of you having a queen is 2/3 times 1/2 = 1/3 (which is what it would have been anyway.....)

5 - 18 days - unless it is a very stupid snail and steps (slithers?) back

and as for left and right - well thats all perception isnt it - like yes and no :)

and Akiko - Happy Birthday xx

AkiToo said...

Thanks for the Birthday wishes, y'all.

Spikey - you got two and a half out of 5.

No-one is even close with number 6 yet.

More please!

Remember, I need proofs of the lot!

sww said...

Here’s hoping this is somewhat to the point of question 6.

The difference between left and right depends on whether left and right refer to adjectives, participles, the present, future or past tense, a third, second or first person, political opinions, brain hemispheres, sides of the road, ends of a football field, batting hands, sides of the Berlin wall, the electromagnetic radiation spectrum, the ends of a map, feet (my left is half a size bigger than my right), the side of the page to start writing from, sides of a theatre or ideas about physics.

For a clear understanding of what is the difference between left and right, it all depends on which way you look at it. The difference is relevant relative to the onlooker; of this am I certain? Well, I am surely certain when I look at it that way.

An answer to this puzzling question is 180 degrees, respectively.

AkiToo said...

Ime:

The point of Question 6, and this is part of the reasoning process, is really this:

How would you explain to a child, the difference between a model of the right-handed molecule Chloro-Bromo-Iodo methane, and it's left-handed counterpart, without reference to feet, hands, 180 degrees, sides of the road, etc?

It is this: Is there a fundamental difference between them as they are obviously not the same to look at? Or is there not? And if so, what is it, and how do you tell one from the other?

I have given far too much away here, but the question still, in it's basic sense, remains, "What is the difference between left and right?"

I STILL don't think anyone will be able to answer this, despite the fact that I have given so many clues here.....Ponder on, wise ones!

Wyman Stewart said...

6) Would you mean they are mirror images? Then you can draw from that the difference, which (I think) is they are asymmetrical. Well, by that I mean, take a pair of gloves, one righthanded and one lefthanded. If you lay the righthand glove atop the lefthand glove you will find the thumb of the righthand glove will lay on the little finger of the lefthand glove. I hope I am stating this correctly or am at least on the right track.

Yes, I think you have now given enough information that most who have a scientific mind will know the answer. Perhaps not me, but others may know. Anyway, if this is what you speak of, it is a very fascinating subject. I think I have even heard our universe has a predilection for being a righthanded universe. Hope I have helped in some small way.

Wyman Stewart said...

Oops!!! Very sleepy here and did not notice your "don't use your hands" admonition. Okay, I seem to recall something about shining polarized light on them will reveal their difference, because the light will be reflected in opposite directions. I think their molecules may also spin in opposite directions. I also think one will react more readily in a chemical reaction than the other. I apologize to one and all for being more longwinded than I am gifted. I DO hope I got this right after taking up all this space. If not, then I look forward to seeing the correct answer.

AkiToo said...

This is the whole point, Wyman. You say "the righthand glove atop the lefthand glove". How do we know that it is not the lefthand glove atop the righthand glove?

You will say "because we call it that" . The question is not about naming which is which.

The question is, can you do it WITHOUT naming things in the human way?

So, in that sense, What exactly IS the difference between "left" ie THAT Chloro-Bromo-Iodo Methane molecule over THERE, and "right" ie THIS one over HERE, because they are obviously different.

What is that difference?

ANYONE - WHAT is that difference?

sww said...

Aki, is the difference that each molecule is always in an individual location?

AkiToo said...

David, if it was perception, we would see the molecules differently depending on what they were doing, or,

Ime, where they are.

Both of you , it is about the properties of this thing we call right-left.

No-one, as yet, apart from Wyman, has even had an intelligent think about it.

Unknown said...

6 is easy - they are spelt differently!

AkiToo said...

Of course, Raquel, very perceptive of you. Stick with the spirit please.

Wyman Stewart said...

:-( Before I go offline to ponder this more, I will venture one more time into this quagmire called Q.6. In the hope of not being redundant in my reply, I suggest the difference in right and left is this: The two are non-superimposable. If you lay one atop the other one, there will be a difference of location, at which location they will be exact opposites.

Now, I am going offline to ponder why we did not bring our polarized flashlight along to make this much easier. Then I will remember what Einstein taught me about "thinking simple" to see if I am missing something basic to this question. Glad I am not in this alone. As the Beatles once said, HELP! comrades.

Wyman Stewart said...

On my way to becoming the next Einstein, my brain was left battered and bruised by a subject called Algebra and I too never got to take Physics in high school. Still have never had any Physics despite a little college. I read a lot on Physics, Astronomy, and related subjects because despite my shortcomings I wish to understand what I can about these fascinating subjects.

Akiko was kind enough to Take Me On and I count that a blessing. Am I avoiding # 6? Yes, for the moment. May one among us have that Aha moment on this question.

AkiToo said...

If you would all read between the lines to the real quertion, it mey help you. thus:

If there is a another way to tell those two molecules apeat other than the phrase "one is the mirror image of the other", is there one, and if there is, what can it possibly be?

No more hints yet, although I do have a few to offer.....

AkiToo said...

No, David, no prize, simply because your answer is self-referential.

Don't you see that what you just said was tantamount to saying "Surely the answer is because there is an answer"?

The question is really "Is there another way of classifying left and right without referring to the other?"

Apologies for the bad spelling in the previous comment as I have been having double vision.

Out-foxed again, Sy?

Wyman Stewart said...

I am on vacation from this problem for this week, though I like David's reply and may have meant to say that or have said it I thought. Let me go with this facetious reply to see if acting stupid leads to intelligence: The way you tell them apart is they do not "look" exactly alike when examined closely. However, looks can be deceiving, I am sure science would say.

If you look it up, I think you will find I am right about "shining polarized light" on the two molecules is an identifiable difference, although maybe not easy to explain to a child. ;-) So, teacher, I think I deserve partial credit at the very least for having answered your question, even if it was not the answer you were looking for. You did not specify "No tools allowed" for solving your mystery. If I am wrong I will put my Dunce Hat on again. I still want to solve it your way, but as mentioned above, I am on vacation from your problem this week.

It has been driving me crazy because I know the answer is going to be SOOOO obvious once I read it. Okay, that was my facetious answer, "They do not look exactly alike." That is where my brain is this week. Seriously, thank you for presenting these problems. They seem to infect the mind until there is some form of resolution/cure.

Wyman Stewart said...

:-) Your Double Vision reminds me of Foreigner. Not that I like the song that much.

To David with chagrin: Yes, I suppose these problems do lead one to circular thinking after a time. Take heart in the fact I now need two Dunce Hats for both sides of my brain, for I applauded your effort with insistence that surely I had thought of that answer at some point, then I gave my own circular answer. Well, at least our Teacher will have a quality notebook of Circular Thinking to use to dissuade future students.

"Ah (my) Grasshopper brain is being called back to vacation by Master Yoda." Okay, I crossed Kung Fu with Star Wars, it could happen! You know, my American Heritage Dictionary gives a better definition for Left than it does Right. So, with sorry help like that, how are we to know the difference between left and right? I can't afford the Oxford Complete Unabrigded Dictionary. "Sigh!" Bye, but glad I am not alone in this.

Wyman Stewart said...

Forgive me, I am leaving after this reply, whatever else comes to mind. I will suggest their orientation in space will be different if they are in the same plane of reference, one will be oriented North, while the other will be oriented South. Of course, being directionally challenged this could be East and West. That is the differing part of their structure will be oriented as suggested, which is my basis for stating it as the whole molecules orientation. I hope this is not circular thinking also, but "Hey everyone, look at the two molecules in your minds eye and that might supply the answer." Hope that helps, for I am not use to being right without lots and lots of time to think on these problems. I better stick to reading. I am thinking too much. Forgive me for posting too many times in one day or even one week.

Wyman Stewart said...

1. I do not frequent pubs, bars, discos, beer joints (as they were disdainfully called in my childhood) or other alcoholic establishments, especially to be quizzed.

2. At least on the American version of "Who Wants To Be A Millionaire" I do much better than here and usually have 4 possible answers to choose from.

3. I think it is about time you reworded the question! I need a new reason for giving the wrong answer and the old courtroom lawyerly thing of "rephrasing the question" sounds good to me. I think science calls this Blame The Question Syndrome.

4. David, I knew she would say you do not need a PhD to answer the question. However, a good cheat sheet might come in handy.

5. If that is all polarised light does, then there is no left and right. Surely left and right is an illusion, if not a delusion. A human construction which can not be proven. I would give some examples, but will wait to be drip-fed more clues.

AkiToo said...

Great kid - Don't get cocky!

You may have won a battle, but it ain't the war. Note the wording of my congrats carefully........

"There is NO WAY to distinguish between "left" from "right" in the WAY WE ALL see it."


and thereby hangs a tale.

Meanwhile, go back to the original five.

Wyman Stewart said...

Congratulations David!!! Way to go! Best of luck with the other questions. Bye!!!