Solve Enjoyable Enigmas with Mr.E's Challenge

[Enigman]

Snowball broke the window. You are .
Who broke it? -I already answered that .

 

[drizzle]

Well, move on to the next Enigmas, I'll do the yard work.

 

[Enigman]

Solve this one first...

Spoiler

Saying what I wrote aloud may help

 

[zoobyshoe]

Next one:[/size]
Y[/size]ou are at your home sitting on the sofa reading a book. Suddenly a snow ball crashes through the window, you look out of the broken* window to see the three brothers from next door -John , Mark and Fred run around the corner and me standing there enjoying the show
You ask me who did it. I write the following thing to you on a scrap of paper "?, he broke your window."
So who would you question/scold/have your yard work done by for free?
(Except me, I am off limits. Oh, and I didn't break your window and am telling the truth- enigmatically though it may be...)
EDIT:*broken.

Spoiler

"?, he broke your window" = "Question Mark, he broke your window."

 

[Enigman]

Yep, ZBS that is correct.

 

[zoobyshoe]

Spoiler

If the person in front of you has a white hat, place your hand on their left shoulder. Otherwise place your hand on their right. Then it doesn't matter what order they get called to reveal their hat color.

Comment and variation of your solution:

Spoiler

They're not called on to give their hat color. They decide when to speak up. Regardless, I think your solution should be counted as correct. I'm afraid Office Shredder will condemn it as "wiseassery," though.

Anyway, your thinking outside the box gave me an idea for another, similar, solution. Hitherto, I've been stuck thinking the last person has to be the sacrificial one who does not call out his hat color with 100% certainty. We could make the first person the sacrificial one, though, by exploiting even more non-prohibited options.

After the line is formed and all the hats are in place, everyone could take a second to check out the hat color of the person in front of them, then they could reach forward, grab the hat off that person's head, and put it on their own head. The first person would be left hatless, and there'd be an extraneous hat at the end of the line, but 99 of them would all now know the color of the hat on their head with 100% certainty. They could call out from front to back or visa versa, depending on which they decided.

I get the sense Office Shredder has some much more mathematical solution in mind. I've been thinking all day and nothing like that has occurred to me.

 

[Enigman]

I get the sense Office Shredder has some much more mathematical solution in mind. I've been thinking all day and nothing like that has occurred to me.

Conciousness solved it: https://www.physicsforums.com/showpost.php?p=4515008&postcount=258
and then modified it: https://www.physicsforums.com/showpost.php?p=4515113&postcount=264

 

[consciousness]

Another one that I love-

You die and the devil says he'll let you go to heaven if you beat him in a game. The devil shows you a round table (perfectly circular). He gives himself and you a huge pile of quarters. He says "ok, we'll take turns putting quarters down, no overlapping allowed, and the quarters must rest on the table surface. We can put the quarters anywhere on the table.The first guy who can't put a quarter down loses." You guys are about to start playing, and the devil says that he'll go first. However, at this point you immediately interject, and ask if you can go first instead. You make this interjection because you are very smart, and you know that if you go first, you can guarantee victory. Explain how you can guarantee victory.

Take your time on this one, easy to understand but challenging to solve .

 

[Enigman]

I think I got it but I don't have the mathamatical proof for it and am just going on intuition...

Spoiler

The first goes into the center (as that is the only unique position) then the rest go diametrically opposite to the 2nd player's ie. devil this will ensure(I think) that all the possible places are already taken up when the final turn of devil comes

I will need some time to come up with the proof (that is of course if I can and if the answer is correct...)
BTW- I am prepared to meet the devil, but whether he is prepared to meet me is an entirely different matter.*
}:-D
*Paraphrasing Churchill

 

[drizzle]

Spoiler

Only an odd number of quarters complete the circle, the odd one being at the center. But I'm too lazy to do the math. :p

On a side note, I don't know why stoichiometry jumped to mind? *shakes head*

 

[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.