Solve Enjoyable Enigmas with Mr.E's Challenge

[Office_Shredder]

Spoiler

Some additional solutions to the walk a mile south, west, north problem. If you find any circle around the souht pole which has circumference 1/n miles for n an integer, you can walk a mile north of that circle, then walk down to the circle, walk around the circle a bunch of times, then walk north again.

As a totally random aside, am I the only person who has a negative reaction to thinking about a blind guy reading a book, and his wife just turns the lights out on him? I realize there's no reason to leave the lights on if he's blind but there's still something very off-putting about it to me

 

[zoobyshoe]

Spoiler

Some additional solutions to the walk a mile south, west, north problem. If you find any circle around the souht pole which has circumference 1/n miles for n an integer, you can walk a mile north of that circle, then walk down to the circle, walk around the circle a bunch of times, then walk north again.]

! Excellent point!

 

[Enigman]

Spoiler

Some additional solutions to the walk a mile south, west, north problem. If you find any circle around the south pole which has circumference 1/n miles for n an integer, you can walk a mile north of that circle, then walk down to the circle, walk around the circle a bunch of times, then walk north again.

Yep, that was what I got too. Its an infinite set.

 

[collinsmark]

Darn it! I was working on this for the last hour, but Zooby beat me to the post.

Spoiler

Obviously, there is the North Pole. That's the only obvious answer. But near the South Pole, with the starting point just a little more than a mile away from the south pole, there exists an infinite number of latitudes that meet the requirement. But not just any latitude, it must meet some heavy restrictions. The starting distance from the South Pole, minus 1 mile, must be the radius of a circle who's circumference is exactly 1 mile divided by any natural number. In other words, that circle's circumference can be 1 mile, 1/2 mile, 1/3 mile, 1/4 mile, etc. Therefore the radius of the circle must be r = [1 mile]/(2πn), where n is a natural number (i.e. n = 1, 2, 3, 4, ...).

Going by the convention that latitudes are negative in the southern hemisphere, these latitudes will all be very near -90^o Now we can calculate out these latitudes, L,

(π/180^o)(90^o + L)r_e - [1 mile] = [1 mile]/(2πn),

where r_e is the radius of the Earth, in units of miles.

A little algebra gives us

L = 90^o(1 + 2πn)[1 mile]/(π²nr_e) - 90^o


[Edit: This answer does rely, in part, on the approximations that sinθ ≈ θ, cosθ ≈ 1, for very small θ (and θ is in units of radians). This is a fair approximation though, since 1 mile is much, much smaller than the circumference of the Earth.]

 

[Enigman]

So, I want to state for the record, I found my answer legitimately before seeing your indiscretion.

Which one? Q&A, Braille or Earth?

I think additional clues should be the sole prerogative of the poster of the enigma, and should only be in response to explicit expressions of frustration by at least two respondents.

So, if I know the answer I can just blurt it out(in spoilers of course) and not give any clues?
Anywho Next one:
A science teacher told his after school class, "Whoever can get this egg into this smaller glass bottle will win no homework for a week! The rules are: the egg has to go into the bottle in one piece, and you can't break the bottle. You can also use anything in the science lab. So, do we have any volunteers?"

A boy raised his hand and the teacher pointed at him. The boy took the egg and looked around the science lab for the things he could use. He saw some writing paper, a pack of matches, some vinegar, a sink, and the glass bottle. By the end of the after school class, the boy had gotten the egg into the smaller bottle.
How did he do it?
[Note that, without doing anything to the egg, the egg can't fit into the bottle.
Also the trick works without vinegar, but I am just copy pasting it from a site after searching for this puzzle.]

 

[zoobyshoe]

Darn it! I was working on this for the last hour, but Zooby beat me to the post.

Spoiler

As Office Shredder pointed out, I missed an infinity of further answers and you didn't, so that makes your answer infinitely better than mine.

 

[zoobyshoe]

Which one? Q&A, Braille or Earth?

South, west, north, same point.

So, if I know the answer I can just blurt it out(in spoilers of course) and not give any clues?

Why should you be giving open, unasked for clues to someone else's enigma? The point of spoilers is so people can avoid reading them if they want and work the solution themselves, despite the fact someone else may already have gotten the right answer. Lack of response doesn't mean everyone is stumped. People have other stuff to do, and may not even have read the riddle yet.

 

[Enigman]

The spherical coordinate thing was barely a clue...And I was trying to get the attention to that Enigma...you people were stretching Braille too much...
Well, get the egg in the bottle now.

 

[consciousness]

Egg and bottle-

I think it should be a hard boiled egg! That was very important.

Spoiler

Put the egg on the mouth of the bottle. Light the paper and use it to heat the neck of the bottle. This will raise the temperature of air inside the neck and create a localized low pressure region there. Since the outside pressure is same there will be a net downward external force acting on the egg, pushing it into the bottle. Vinegar can be used to decrease friction I guess. I heard this one many times.

 

[Enigman]

Correct.
But

Spoiler

the egg doesn't need to be boiled, vinegar eats away the shell making it softer- but I have done it without either of these in 5th grade ...but it probably depends on the size of the mouth of bottle. Also burning paper should be inside the bottle to make it more efficient.

Next one:
Teacher wants the egg back out of the bottle, she needs the bottle for storing chemicals*. Without making a mess bring the egg out of bottle.
EDIT: Do it such that you don't affect the egg at all (except getting it out of the bottle). No boiling. *Not a hint.

 

[consciousness]

Spoiler

The effect of vinegar is very cool. It dissolves the egg shell giving you a plump egg just held together by a membrane, like a water balloon. This gives me the following idea-
Just pour a very hypertonic solution into the bottle. All the water inside should leave the egg giving you a small egg surrounded by a big membrane. Then pour it all out of course.

 

[Enigman]

Actually to do that you would need glacial acetic acid not just vinegar. Vinegar can only soften it so much in the short time of a few hours. To completely get rid of external shell you need 3-4 days, though it depends on concentration- I had to wait till a week to get my blood egg...(Hypertonic solution to take the moisture out and then red hypotonic solution). But it is a viable solution if time wasn't a constraint.
There is a simpler solution which doesn't involve any solutions...
Now I have got one strike after the next one (if there is one) I start giving hints.

 

[Enigman]

I heard this one many times.

I am quite sure, but what I wanted was an egg in a bottle; which you gave me...
Clichés are not my niche.
Mr.E

 

[consciousness]

Cool the bottle or heat the surroundings. There should be many ways to do this...

 

[Enigman]

mmm...nope...you don't have a fridge or anything to heat the surroundings with.
But you are on the right track, sort of. There is an easier and more efficient way of doing what you are trying to do...

 

[Enigman]

Spoiler

You don't need anything except the bottle and egg. No equipments at all!

 

[Enigman]

Sorry zoob et al. I am BORRRRRED...

Spoiler

to put the egg in the bottle you create a low pressure in the bottle. Now do the opposite. Take a deep breath and think...

 

[Enigman]

Spoiler

Blow!

And out I bow.

 

[consciousness]

Spoiler

The trick is to blow into the bottle when it is inverted. The burst of air bounces the egg before it reseals the bottle. This has two effects-
1)It as you say it increases the pressure inside the bottle.
2)(More important IMO) Creates low pressure at the mouth of the bottle by Bernoulli's equation.

An open ended question-

A black man, dressed in black, is crossing a road. He's blind and deaf. A truck is speeding towards him at great speed, with its lights turned off (probably a crazy driver). The starlight is very faint. The street lamps are also off and there's no moonlight. When the truck is about to hit the man, the driver hits the brakes and manages to stop just a few centimeters from him. How?

 

[Enigman]

Er...

Spoiler

is Sunlight considered to be starlight?

 

[consciousness]

Er...

Spoiler

is Sunlight considered to be starlight?

Technically the sun is a star but not in the context of the puzzle.

 

[Enigman]

Spoiler

Well, it was a day or there were lightning flashes or the driver had to pee or there was a helicopter overhead with search-lights or the pedestrian was wearing glow-in-the-dark (er...phosphorescent?) clothes or it was the ALIENS!

 

[consciousness]

The answer-

Spoiler

Yes it was day.

 

[Enigman]

Well, you did mention open-ended...

 

[consciousness]

You forgot night vision goggles

 

[Enigman]

Aliens trump all.

 

[consciousness]

A physics enigma-

Two identical spheres receive identical amounts of thermal energy, the heat transfer occurring so quickly that none is lost to the surroundings. If they begin at the same temperature, but one is on a table and the other is suspended by a string, will the spheres still have the same temperature immediately after the quick addition of thermal energy?

 

[Office_Shredder]

Spoiler

Alternate solution: The man was standing at the edge of the parking spot the truck was driving to

 

[consciousness]

Spoiler

Alternate solution: The man was standing at the edge of the parking spot the truck was driving to

That won't work...he was crossing a road.

 

[Office_Shredder]

Spoiler

Trucks can park on the side of the street though

 

[drizzle]

The blind man sings.. Loudly. :p

 

[Enigman]

The blind man sings.. Loudly. :p

He's deaf. Deaf people don't sing.

 

[consciousness]

Finer point about man crossing road-

Spoiler

I added the bit about the starlight to make the problem harder. Starlight does reach us during the day although it is overpowered by the sun.

Solve this one. It is kinda hard, but if you solve it you will feel really smart.(For a day that is )

Two identical spheres receive identical amounts of thermal energy, the heat transfer occurring so quickly that none is lost to the surroundings. If they begin at the same temperature, but one is on a table and the other is suspended by a string, will the spheres still have the same temperature immediately after the quick addition of thermal energy?

 

[collinsmark]

A physics enigma-

Two identical spheres receive identical amounts of thermal energy, the heat transfer occurring so quickly that none is lost to the surroundings. If they begin at the same temperature, but one is on a table and the other is suspended by a string, will the spheres still have the same temperature immediately after the quick addition of thermal energy?

Spoiler

Yes, they will have the same temperature immediately after the quick addition of thermal energy -- a transfer that was such that no heat was exchanged with the surrounding environment.

This assumes that the string and the table are part of the environment, and thus were not involved in any heat transfer. This includes any possible ionization effects: the string and table are part of the environment and were not affected by the heat transfer at all -- at least not yet.

This neglects any quantum effects of the different configurations, which wouldn't be measurable anyway if the spheres are at all larger than microscopic.

This also neglects any differences caused by general relativity (as opposed to Newtonian gravity), which wouldn't even come close to being measurable assuming the these are regular old objects, here on Earth.

And lastly it assumes that none of thermal energy is transferred to the surroundings via thermal vibrations -- again, no energy is transferred to the surroundings, and that includes the string and table.

Edit: Oh, and of course I don't mean that the spheres will have the same temperature that they started with. I mean they will have the same temperature as each other.

 

[collinsmark]

Two identical spheres receive identical amounts of thermal energy, the heat transfer occurring so quickly that none is lost to the surroundings. If they begin at the same temperature, but one is on a table and the other is suspended by a string, will the spheres still have the same temperature immediately after the quick addition of thermal energy?

Spoiler

Yes, they will have the same temperature immediately after the quick addition of thermal energy -- a transfer that was such that no heat was exchanged with the surrounding environment.

This assumes that the string and the table are part of the environment, and thus were not involved in any heat transfer. This includes any possible ionization effects: the string and table are part of the environment and were not affected by the heat transfer at all -- at least not yet.

This neglects any quantum effects of the different configurations, which wouldn't be measurable anyway if the spheres are at all larger than microscopic.

This also neglects any differences caused by general relativity (as opposed to Newtonian gravity), which wouldn't even come close to being measurable assuming the these are regular old objects, here on Earth.

And lastly it assumes that none of thermal energy is transferred to the surroundings via thermal vibrations -- again, no energy is transferred to the surroundings, and that includes the string and table.

Edit: Oh, and of course I don't mean that the spheres will have the same temperature that they started with. I mean they will have the same temperature as each other.

Spoiler

That last post also assumed that the two spheres were identical at the time the heat transfer, and at the time temperature measurements were taking place.

But now I think I see where this riddle is going.

I think the riddle meant to say, "the spheres are not ideal sphere's. Instead they are practical spheres that are not completely rigid. And they are identical before being placed on the string or the table, but not necessarily after."

If that were the case then the sphere hanging on the string would tend to "stretch out" ever so slightly, while the sphere on the table would tend to compress upon itself every so slightly. Thus the spheres wouldn't technically be identical anymore at the time they were hanging from a string or sitting on a table.

In that case, the sphere on the table would be slightly denser, containing a slightly larger energy density, and be slightly hotter.

 

[consciousness]

collinsmark, this is a very practical riddle. Nowhere in the problem statement have the spheres been called "ideal". You have to take practical considerations into mind while solving this one. You are on the right track, almost.

Spoiler

I don't understand the last part about compression though. Why would it compress? I think you are ignoring a very practical consideration here.

 

[zoobyshoe]

I have not been contributing enough riddles, so I went to the library today and got a book.

Here's one:

"An ordinary cyclist travels up and down a hill. Going up, she maintains a constant speed of 10 mph. It takes her 1 hour to get to the top. Assuming the hill is symmetric, what speed must she maintain on the way going down if she wishes to average 20 mph?"

 

[drizzle]

Spoiler

∞?

 

[Office_Shredder]

consciousness, I have trouble reconciling "two identical spheres" and "these spheres are not perfect spheres".

 

[zoobyshoe]

Your light switch is on the other side of the room from your bed. However, you make a bet that you can turn the light off and jump in bed before the room gets dark. No timers are involved. How do you win this bet without violating SR?

 

[zoobyshoe]

Boomerang Ball:

You throw a ball as hard as you can. It doesn't hit anything, and no strings or rubber bands are attached to it, yet, it comes right back to you. How can this be?

 

[zoobyshoe]

You are standing on a hard concrete floor and you have no cushioning to use. You bet someone you can drop a raw egg 4 feet without it breaking. You promise you won't even drop it on your feet. How do you win this bet?

 

[drizzle]

Boomerang Ball:

You throw a ball as hard as you can. It doesn't hit anything, and no strings or rubber bands are attached to it, yet, it comes right back to you. How can this be?

Spoiler

Is there not a word for 'vertical relative to Earth's surface'? In my language there's vertical, and there's this word which means vertical relative to Earth's surface..

 

[Enigman]

Spoiler

Is there not a word for 'vertical relative to Earth's surface'? In my language there's vertical, and there's this word which means vertical relative to Earth's surface..

Spoiler

...Up?

 

[drizzle]

Lol

 

[zoobyshoe]

Spoiler

Is there not a word for 'vertical relative to Earth's surface'? In my language there's vertical, and there's this word which means vertical relative to Earth's surface..

Spoiler

In physics any line that is perpendicular to a given surface is "normal" to that surface. The word "up" would have done just fine, though I wish it hadn't been blurted out without spoilers.

 

[Enigman]

I have not been contributing enough riddles, so I went to the library today and got a book.

Here's one:

"An ordinary cyclist travels up and down a hill. Going up, she maintains a constant speed of 10 mph. It takes her 1 hour to get to the top. Assuming the hill is symmetric, what speed must she maintain on the way going down if she wishes to average 20 mph?"

Spoiler

teleportation allowed?

Your light switch is on the other side of the room from your bed. However, you make a bet that you can turn the light off and jump in bed before the room gets dark. No timers are involved. How do you win this bet without violating SR?

Spoiler

use a torch? It was a day?

You are standing on a hard concrete floor and you have no cushioning to use. You bet someone you can drop a raw egg 4 feet without it breaking. You promise you won't even drop it on your feet. How do you win this bet?

Spoiler

Er, catch it before it falls?

 

[consciousness]

My question was somewhat ambiguous. I have edited it now.

Two identical metal spheres receive identical amounts of thermal energy, the heat transfer occurring so quickly that none is lost to the surroundings. If they begin at the same temperature, but one is on a table and the other is suspended by a string, will the spheres still have the same temperature immediately after the quick addition of thermal energy?

I have another answer for raw egg-

Spoiler

Concrete floors aren't so easily broken!

Cyclist-

Spoiler

Its not possible!

Hint for spheres-

Spoiler

Metals appreciably expand on heating

 

[collinsmark]

My question was somewhat ambiguous. I have edited it now.

Two identical metal spheres receive identical amounts of thermal energy, the heat transfer occurring so quickly that none is lost to the surroundings. If they begin at the same temperature, but one is on a table and the other is suspended by a string, will the spheres still have the same temperature immediately after the quick addition of thermal energy?
[...]
Hint for spheres-

Spoiler

Metals appreciably expand on heating

Spoiler

Assuming now that both spheres maintain identical densities with respect to each other, and have positive thermal expansion coefficients (unlike zirconium tungstate), then the sphere on the string will be the hotter of the two.

Conservation of energy is at play here. The average height of the sphere on the table will rise up a bit, while the sphere on the string will be lowered. The difference in potential energy equates to work done by a heat engine, essentially. The end result is, for the moment at least, the sphere that gains potential energy is the colder of the two, meaning that the sphere on the string is hotter than the one on that table, since the sphere on the string lost potential energy and the sphere on the table gained potential energy in the process.

 

[consciousness]

Spoiler

Assuming now that both spheres maintain identical densities with respect to each other, and have positive thermal expansion coefficients (unlike zirconium tungstate), then the sphere on the string will be the hotter of the two.

Conservation of energy is at play here. The average height of the sphere on the table will rise up a bit, while the sphere on the string will be lowered. The difference in potential energy equates to work done by a heat engine, essentially. The end result is, for the moment at least, the sphere that gains potential energy is the colder of the two, meaning that the sphere on the string is hotter than the one on that table, since the sphere on the string lost potential energy and the sphere on the table gained potential energy in the process.

Correct.