Solve Enjoyable Enigmas with Mr.E's Challenge

[consciousness]

Suppose you coat a tennis ball with glue. What is the maximum number of tennis balls that can be attached directly to this sticky surface?

Spoiler

This is another way of asking "What is the coordination number/ligancy in a FCC/HCP lattice? The answer is 12.

 

[zoobyshoe]

Spoiler

This is another way of asking "What is the coordination number/ligancy in a FCC/HCP lattice? The answer is 12.

Spoiler

I don't know what you just said, but, yes, the correct answer is 12. Office Shredder would have been correct but he decided to put his money on the answer being a perverse case where you deform things and fit 13 in.

 

[Enigman]

He was talking about atomic crystal packing, FCC or face-centred cubic arrangement of atoms is the most efficient packing of them all. Alternatively called H.C.P.- hexagonal close packing. Another honourable mention would be the kissing number problem of which your enigma is a special case of (the 3-d case). http://en.wikipedia.org/wiki/Kissing_number_problem

 

[Enigman]

This one should be a quickie-
You are given two plastic cups taped together at the rim- making a closed cylinder of sorts, inside it there are two table tennis balls. Your goal is to get the balls at opposite end of the cups. You are not allowed to break or untape anything.

 

[consciousness]

This one should be a quickie-
You are given two plastic cups taped together at the rim- making a closed cylinder of sorts, inside it there are two table tennis balls. Your goal is to get the balls at opposite end of the cups. You are not allowed to break or untape anything.

Spoiler

Rotate the cylinder w.r.t. to symmetric axis

 

[Enigman]

Correct. (Nitpicking: there are two symmetrical axis)

 

[Office_Shredder]

Spoiler

I don't know what you just said, but, yes, the correct answer is 12. Office Shredder would have been correct but he decided to put his money on the answer being a perverse case where you deform things and fit 13 in.

Spoiler

One of the reasons that 13 was considered a legitimate possibility is that if you take fourteen oranges, and put one in the middle, you can squeeze thirteen of them to all be adjacent to that orange at the same time. If you had asked for billiard balls or something the answer would be 12, but I think tennis balls are squishy enough that the correct answer should be 13.

 

[Enigman]

A monk climbs to the top of a certain mountain with unequal speeds and random stops of random durations, he reaches the top at the sunset of the 13th day from the start. After meditating there for a week, he starts climbing down the mountain at the sunrise with unequal speeds and random stops. The speed while climbing down is obviously greater than speed climbing up. Assuming that he follows the exact same path for both journeys prove that there exists a time of day where the monk was at the same position on the path for both journeys.

 

[consciousness]

I modified Enigman's question, making it slightly more difficult-

You have a long metal cylinder say 1 meter in length. It is known that there are 2 table tennis balls(of known dimensions) somewhere inside it. Devise a method to guarantee that the balls are put at opposite ends of the cylinder.

 

[consciousness]

A monk climbs to the top of a certain mountain with unequal speeds and random stops of random durations, he reaches the top at the sunset of the 13th day from the start. After meditating there for a week, he starts climbing down the mountain at the sunrise with unequal speeds and random stops. The speed while climbing down is obviously greater than speed climbing up. Assuming that he follows the exact same path for both journeys prove that there exists a time of day where the monk was at the same position on the path for both journeys.

Spoiler

He was at the end of the path at 6 o clock for both journeys.

 

[Enigman]

For #409

Spoiler

1)hold the pipe vertically.
2)turn it over
3)1/2 - 2r=1/2 gt^2
4)(1-4r/g)^0.5=t
5)At t start spinning the tube in a horizontal plane like a mad man.( would work in vertical plane but you will have to spin harder)

For #410
No he wasn't. Position is with respect to the path. At 6:00 pm on first journey he was at top of mountain on second he was at the bottom of it.
No word play involved.

 

[consciousness]

For #409

Spoiler

1)hold the pipe vertically.
2)turn it over
3)1/2 - 2r=1/2 gt^2
4)(1-4r/g)^0.5=t
5)At t start spinning the tube in a horizontal plane like a mad man.( would work in vertical plane but you will have to spin harder)

Hehe that will undoubtedly work. But if you can do that you probably deserve an Olympic gymnastics medal for amazing timing and dexterity! There is an easier method.

About monk-

Spoiler

I meant that he was on the path near the mountain at 6 o clock (sunset/sunrise), once while going and once while coming.

Edit: Okay you are distinguishing between AM and PM.

 

[collinsmark]

A man is running home, but he's afraid to get there, because there is another man already there who is wearing a mask and doing a "job."

What is the masked man's occupation?

Hint: there is a diamond involved.

Spoiler

I'm thinking it's a workman wearing a dust mask drilling into masonry with a diamond tipped drill.

No, that's not correct.*

Here's a hint though: people are watching him.

*[Edit: okay, so maybe it fits, but there's a better answer.]

 

[Enigman]

Hehe that will undoubtedly work. But if you can do that you probably deserve an Olympic gymnastics medal for amazing timing and dexterity! There is an easier method.

Spoiler

hold the pipe vertically
slowly turn the pipe into a horizontal plane
start spinning with the axis at 2r

 

[zoobyshoe]

Here's a hint though: people are watching him.

People are watching the masked man?

 

[Office_Shredder]

On the masked man:

Spoiler

The two men are married (hence the diamond). The job the man at home is doing is that he does webcam shows for money and wears a mask while doing them - the man returning home was surfing online for pornography while at work and found his husband doing these shows, and is running home to confront him in the act.

It's a reach but I figured I'd post it.

 

[zoobyshoe]

I modified Enigman's question, making it slightly more difficult-

You have a long metal cylinder say 1 meter in length. It is known that there are 2 table tennis balls(of known dimensions) somewhere inside it. Devise a method to guarantee that the balls are put at opposite ends of the cylinder.

Spoiler

Float the cylinder in a tank of hot water without letting it rotate. The hot side should expand. The two ends will then be elevated and the balls should center themselves, one on each side of the mid line. Carefully rotate the cylinder 180 (on the axis that goes through the centers of the end circles). One ball should roll to one end and the other ball to the other end.

 

[consciousness]

Spoiler

hold the pipe vertically
slowly turn the pipe into a horizontal plane
start spinning with the axis at 2r

Yes correct. You can also-

Spoiler

Rotate with axis at an end to ensure that the balls collect at the other end.

Spoiler

Float the cylinder in a tank of hot water without letting it rotate. The hot side should expand. The two ends will then be elevated and the balls should center themselves, one on each side of the mid line. Carefully rotate the cylinder 180 (on the axis that goes through the centers of the end circles). One ball should roll to one end and the other ball to the other end.

That is a nice solution. There is a simpler solution similar to Enigman's original question's solution also.

 

[zoobyshoe]

Yes correct. You can also-

Spoiler

Rotate with axis at an end to ensure that the balls collect at the other end.

Spoiler

I don't understand. Isn't the goal to end up with one ball at each separate end?

 

[Enigman]

Spoiler

I don't understand. Isn't the goal to end up with one ball at each separate end?

You don't have to spoiler everything...
No, conciousness' method would not work if

Spoiler

the axis passes through the end of tube but if if the axis is somewhere between the center of mass of the spheres it would get the job done.

Now let's work on collinsmarks' diamond mask enigma...
Thinking out loud-

Spoiler

Man A

1. Mask uses- hide identity/ protects the face/sports/decorational/medical/torture/religious
2. Spectators (plural, more than one) watching whom? A, B or both?
3. "Job"
4. At home

Man B

1. Afraid.
2. Running towards home
3. Not at home
4. Afraid because A's doing a job
5. Apostrophes around "job"
6. Implies it would not usually be called job?

mmm...Obvious answer ruled out by A 2
Mention of diamond. Gem? With whom? A or B? Or shape? Rhombus? Playing cards?
I am drawing a serious blank...Anyone any ideas? I am certain the diamond is more of a misdirection than a hint, though the spectators thing should be a hint.

 

[consciousness]

Spoiler

I don't understand. Isn't the goal to end up with one ball at each separate end?

Yes, this is the first step towards that goal. Second step is same as in Enigman's solution.

 

[consciousness]

Possible solution to mask enigma-

Spoiler

The running man is a thief. He stole a diamond ring from his wife's sister and was planning to sell it for cash. He has hidden the ring under the bed etc. away from his wife. He was working peacefully when he remembered that a pest control man would be coming to his home that day. Realising that the probability of his wife discovering the theft would rise exponentially if he started shifting stuff, he runs towards home to hide the ring somewhere else. He is afraid because the discovery might already have been made.
Notes-
The pest control man is masked.
His wife will recognise the the ring if she sees it.
The man is not too smart to hide the ring there.
His wife and children are the spectators.

 

[Enigman]

Too complicated conciousness...Enigma doesn't give enough data to conclude all that. I think we will all be face-palming when we get the solution and go "Doh!"...
- though you may be still right but the enigma says he is afraid of going in there not afraid of what might happen if he did not get there...

 

[consciousness]

His wife might be waiting for him with a rolling pin though!
BTW I don't think we can solve problems of this nature without making assumptions...the trick is to make reasonable ones.

 

[zoobyshoe]

You don't have to spoiler everything...
No, conciousness' method would not work if

Spoiler

the axis passes through the end of tube but if if the axis is somewhere between the center of mass of the spheres it would get the job done.

Spoiler

We don't know the diameter of the cylinder. It could be large enough that both balls can rest against an end circle side by side in a line perpendicular to the length of the pipe.

Edit:

Spoiler

More specifically, we don't know the inside diameter of the cylinder. That makes knowing the ball dimensions moot.

 

[collinsmark]

A man is running home, but he's afraid to get there, because there is another man already there who is wearing a mask."

What is the masked man's occupation?

I reworded the question slightly removing the emphasis on "job." suffice it to say the masked man is at his occupation at the time.

People are watching the masked man?

Yes.

On the masked man:

Spoiler

The two men are married (hence the diamond). The job the man at home is doing is that he does webcam shows for money and wears a mask while doing them - the man returning home was surfing online for pornography while at work and found his husband doing these shows, and is running home to confront him in the act.

It's a reach but I figured I'd post it.

I'm going to have to go with "no" on that.

----------------------
Here is another clue:

Spoiler

The riddle is culturally biased insofar that exposure to such professions is most probable if one lives in the United States. That said, it's not completely limited to the United States. It's also possible that the situation is happening in Cuba, Japan, Australia, and I think even the United Kingdom, among other possible countries.

 

[Enigman]

Spoiler

We don't know the diameter of the cylinder. It could be large enough that both balls can rest against an end circle side by side in a line perpendicular to the length of the pipe.

Edit:

Spoiler

More specifically, we don't know the inside diameter of the cylinder. That makes knowing the ball dimensions moot.

er... just shake it till you feel balls are in a line...
Any ideas about collinsmark's puzzle? Last time I was this lost was the chinese forensics enigma...darned baseball...

Where is that occam's razor when you need it?

 

[collinsmark]

Any ideas about collinsmark's puzzle? Last time I was this lost was the chinese forensics enigma...darned baseball...

Where is that occam's razor when you need it?

I think you just got it.

 

[zoobyshoe]

Mask:

Spoiler

"Home" is home plate in the game of baseball. The man with the mask he fears is the catcher: is someone throws the catcher the ball before the man get's "home" the man will be "out". Baseball is played on a "diamond".

 

[collinsmark]

Mask:

Spoiler

"Home" is home plate in the game of baseball. The man with the mask he fears is the catcher: is someone throws the catcher the ball before the man get's "home" the man will be "out". Baseball is played on a "diamond".

Yes, that's right.

Spoiler

The man in the mask is a professional baseball player, specifically the catcher on a professional baseball team. The running man is also a professional baseball player, although his specific position on the team is arbitrary.

[Edit: I also would have accepted "umpire."]

 

[Enigman]

That awkward moment when you realize that you are an idiot...
Next time I don't get one- my answer is baseball.
Anyway the answer to this is definitely not baseball:

A monk climbs to the top of a certain mountain with unequal speeds and random stops of random durations, he reaches the top at the sunset of the 13th day from the start. After meditating there for a week, he starts climbing down the mountain at the sunrise with unequal speeds and random stops. The speed while climbing down is obviously greater than speed climbing up. Assuming that he follows the exact same path for both journeys prove that there exists a time of day where the monk was at the same position on the path for both journeys.

 

[zoobyshoe]

Monk question:

You are saying that there is some specific time of day, like, say, 2:40 P.M. when it is guaranteed the monk will be at the very same point on the path going down the mountain as he was going up the mountain?

 

[Enigman]

I am asking for a proof that there will exist a time of day when the monk is at the same point on the path on both journeys. The time of day can be any thing so can be the point on the path - depending on the monk and his various whimsical speeds.
Hint: The speed while climbing down is obviously greater than speed climbing up- Just given to confuse you.

 

[zoobyshoe]

The time of day can be any thing...

So, "time of day" could be as vague as "morning," "afternoon," or "night"?

 

[Enigman]

No- 2:14:35 pm something like that.
Time of day could belong to the whole range of 6:00 am to 6:00 pm* and would be determined how the monk decides to carry out his journeys.**
*assuming sunrise and sunset at those times.
EDIT-**the proof should hold for all cases- all possible speeds and combined with all possible breaks of all possible durations.
Its really not a mathematical proof. Think out of the box...you do remember what happens to the cats in the box...

 

[zoobyshoe]

Time of day could belong to the whole range of 6:00 am to 6:00 pm* and would be determined how the monk decides to carry out his journeys.**
*assuming sunrise and sunset at those times.

The monk only travels during daylight hours, then?

 

[Enigman]

Yes, but it doesn't really matter all that is of significance is both the trips start and end at the same time of day/night...

 

[zoobyshoe]

...all that is of significance is both the trips start and end at the same time of day/night...

Both trips have to start at sunrise and end at sunset?

 

[Enigman]

The only essential thing is that both of the journeys start at the same time of the day and the monk does complete both trips; anything else is extraneous.
There is no math involved, just some elegant reasoning.

 

[zoobyshoe]

You can see for yourself you left this "essential" fact out of your statement of the enigma:

A monk climbs to the top of a certain mountain with unequal speeds and random stops of random durations, he reaches the top at the sunset of the 13th day from the start. After meditating there for a week, he starts climbing down the mountain at the sunrise with unequal speeds and random stops. The speed while climbing down is obviously greater than speed climbing up. Assuming that he follows the exact same path for both journeys prove that there exists a time of day where the monk was at the same position on the path for both journeys.

There's nothing to indicate the first journey was started at the same time of day the second was.

 

[Enigman]

oops...sorry.
Okay rephrasing the question:
A monk climbs to the top of a certain mountain starting at sun-rise with unequal speeds and random stops of random durations, he reaches the top at the sunset of the same day. After meditating there for a week, he starts climbing down the mountain at the sun-rise with unequal speeds and random stops. Assuming that he follows the exact same path for both journeys prove that there exists a time of day where the monk was at the same position on the path for both journeys.
(Sorry again...should never trust the net to give accurate statements...I should have phrased it myself but I just couldn't remember the wordings...)
EDIT:Although the way the enigma was previously stated is solvable and is similar to what I had in mind...I can't decide which phrasing is easier...but 13 day thing may make things more complicated so let's stick to this one

 

[Enigman]

Just to be clear the previous version won't need the " same time of the day" constraint to be solved.
I think the one in the last post is easier compared to that...(I just assumed that the statement from the web was the same thing as what I had in mind...) But these are just technicalities...
As a compensation for the confusion a hint:

Spoiler

Think of the two trips simultaneously...

 

[drizzle]

Spoiler

On about 1/3 of the path on the way up?

 

[zoobyshoe]

oops...sorry.
Okay rephrasing the question:
A monk climbs to the top of a certain mountain starting at sun-rise with unequal speeds and random stops of random durations, he reaches the top at the sunset of the same day. After meditating there for a week, he starts climbing down the mountain at the sun-rise with unequal speeds and random stops. Assuming that he follows the exact same path for both journeys prove that there exists a time of day where the monk was at the same position on the path for both journeys.

You specify that he starts the first trip at sunrise and reaches the top at sunset. You also specify that he starts the second trip at sunrise, but there is no destination time given for this return trip. Is the time he finishes the second trip immaterial?

 

[Enigman]

Nope. It doesn't matter.
EDIT: and the fact that he reaches at sunset is pretty useless too...

 

[Enigman]

Spoiler

On about 1/3 of the path on the way up?

Depends on his whimsy...it might be anywhere...What I ask for is a proof that it will happen.

 

[drizzle]

Spoiler

I have a feeling that it will never happen, as the path he follows starts from one end of the mountain and ends on the other side of it.

 

[Enigman]

He follows the exact same path i.e. he retraces his path from the opposite direction. And it will happen.

 

[Enigman]

Spoiler

Think of the two trips simultaneously...

Well? What happens?

 

[drizzle]

Are we talking about a single monk here?