Solve Enjoyable Enigmas with Mr.E's Challenge

[Enigman]

$$ [ \frac {\pi R^2} {\pi r^2}]=2k+1$$
$$ [ \frac { R^2} {r^2}]=2k+1$$
for any k in N
mmm..why?

EDIT: Actually the above whole thing is wrong.
I implicitly assumed that the gaps between coins won't sum up to area of more than one coin...

 

[Office_Shredder]

conciousness had essentially the solution I was thinking of, but that solution of yours zooby is pretty awesome. I just figured it was silly if you could literally tell the person in front of you what color they should say.

For the devil one

Spoiler

Put the first quarter in the middle, then just mirror his moves across the table

I actually took a geometry elective in high school where this was the very first question the teacher asked. There are also two out of the box solutions I see from the wording of this particular puzzle:

Spoiler

Steal the devil's quarters, then make your move (I know this one is lame)

Spoiler

The devil said you take turns putting quarters down, so if the table is small enough, put down all your quarters in a manner such that no additional quarter may be laid. The devil then takes his turn and loses

As for the original solution I was thinking of for the black/white hat one:

Spoiler

The person in the back calls out black if he sees an odd number of black hats in front of him, white if he sees an even number. The person in front of him can deduce from that which color he is wearing, and calls it out. The person in front of him can then deduce which color he is wearing, and calls it out. Etc.

 

[Enigman]

Here is one just for a bit of fun- Get Off The Earth(1898) by Sam Loyd
It was printed on two pieces of card and sold more than 10 million copies. When the discs are set one way there are 13 characters, but when they move, one of the people disappears!

-http://www.murderousmaths.co.uk/

 

[consciousness]

for the original solution I was thinking of for the black/white hat one:

Spoiler

The person in the back calls out black if he sees an odd number of black hats in front of him, white if he sees an even number. The person in front of him can deduce from that which color he is wearing, and calls it out. The person in front of him can then deduce which color he is wearing, and calls it out. Etc.

ohhh... awesome.

Enigman, your intuition is essentially correct. A mathematical proof is not required, the solution can be given by making statements.

Gad,

Spoiler

I don't think that it is compulsory that the number of quarters will be odd if one is kept at the center. If we do exactly what Enigman has written then certainly the number will be odd though.

 

[zoobyshoe]

Devil's game:

Spoiler

Each row of coins around the center coin will be a hexagon. A hexagon will always be comprised of an even number of coins. By insisting on setting the first, center coin, you force the devil to start each hexagon leaving yourself as the person who will complete it. When the table is too full for another whole hexagon, you are still forcing him to start the filling in, and you will still be the last person who can lay a coin, since the number of fill coins will be some multiple of 6; an even number.

 

[Enigman]

Actually ZBS, the devil could manipulate the distance between two coins making it impossible to make a regular hexagon.

 

[zoobyshoe]

Actually ZBS, the devil could manipulate the distance between two coins making it impossible to make a regular hexagon.

Alas, that is true, but it doesn't matter: the hexagon scenario (most possible space covered) proves that, regardless of what pattern he starts, you will be the one to finish it.

 

[consciousness]

Figure illustrating the solution I had in mind. Blue circles are quarters put by us and red ones by the devil.
https://www.desmos.com/calculator/zevwpq9etd

 

[Enigman]

Next one-
If this is a question, what is the answer?
^{__probably the silliest puzzle I know}

 

[consciousness]

Next one-
If this is a question, what is the answer?
^{__probably the silliest puzzle I know}

Spoiler

If that is a question then this is an answer!

A man was sitting in a room, reading a book, when his wife entered the room and switched off the light. Although this occurred at night, and the room was now pitch dark, the man continued reading as though nothing had happened. How could he do this ?

 

[Enigman]

Spoiler

Blind.Braille.

 

[consciousness]

Right you are! BTW is my answer what you were expecting?

A classic one-

How many places are there on the Earth that one could walk one mile south, then one mile west, then one mile north and end up in the same spot? to be precise, let's assume the Earth is a solid smooth sphere, so oceans and mountains and other such things do not exist. you can start at any point on the sphere.

Read this after you think you have got it-

Spoiler

There is more than one

 

[Enigman]

Right you are! BTW is my answer what you were expecting?

If that was a question you gave the correct answer.

A classic one-

How many places are there on the Earth that one could walk one mile south, then one mile west, then one mile north and end up in the same spot? to be precise, let's assume the Earth is a solid smooth sphere, so oceans and mountains and other such things do not exist. you can start at any point on the sphere.

Read this after you think you have got it-

Spoiler

There is more than one

Crooked and Evil...I like that.
I got it(I think) but I will let the others ponder it a bit...

 

[zoobyshoe]

Spoiler

If that is a question then this is an answer!

A man was sitting in a room, reading a book, when his wife entered the room and switched off the light. Although this occurred at night, and the room was now pitch dark, the man continued reading as though nothing had happened. How could he do this ?

Spoiler

He must have been blind and was reading braille. Issues like this come up in the movie Ray[/], about Ray Charles.

 

[Enigman]

You seem to be missing an i...*
EDIT:* in the italics tag in your post I mean.
There are infinite solutions to the enigma(#292) (aside from the obvious one point) the solution becomes easier when you think in terms of spherical coordinates- but that's just my opinion.

 

[lisab]

Spoiler

He didn't have to be blind, just reading Braille.

 

[Enigman]

A classic one-

How many places are there on the Earth that one could walk one mile south, then one mile west, then one mile north and end up in the same spot? to be precise, let's assume the Earth is a solid smooth sphere, so oceans and mountains and other such things do not exist. you can start at any point on the sphere.

Read this after you think you have got it-

Spoiler

There is more than one

Quoting it just for clarity...
(Originally by conciousness.)
(making sure people have seen this one.)

 

[zoobyshoe]

A classic one-

How many places are there on the Earth that one could walk one mile south, then one mile west, then one mile north and end up in the same spot? to be precise, let's assume the Earth is a solid smooth sphere, so oceans and mountains and other such things do not exist. you can start at any point on the sphere.

Read this after you think you have got it-

Spoiler

There is more than one

Spoiler

There is some circle north of the south pole whose circumference is one mile. With the south pole as the center of that circle, the distance from the south pole to that circle is exactly 1/pi/2 miles, and approximately .159 miles from the south pole.

Starting at any point one mile north of that circle, you can walk one mile south, one mile west around the circle, and then one mile north, and arrive back at the same point you started from. All the points that are one mile north of that circle constitute another circle which has the south pole as its center and an exact radius of 1 + 1/pi/2 miles (an approximate radius of 1.159 miles). Any point on this second circle fulfills the conditions of the riddle, and, since there are infinitely many points in the circumference of a circle, there are infinitely many "places" on Earth from which you can walk south one mile, west one mile, north one mile, and end up at the same point from which you started. The other case is the north pole, of course.

 

[zoobyshoe]

You seem to be missing an i...*
EDIT:* in the italics tag in your post I mean.
There are infinite solutions to the enigma(#292) (aside from the obvious one point) the solution becomes easier when you think in terms of spherical coordinates- but that's just my opinion.

I went out to have coffee, solved it while I was having coffee, then returned to find out you'd blurted out the answer without spoilers.

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

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.

 

[zoobyshoe]

Spoiler

He didn't have to be blind, just reading Braille.

Spoiler

Good point! And one I should have considered, because I know a woman who can see but who works with blind people and can read braille perfectly well.

 

[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...