Solve Enjoyable Enigmas with Mr.E's Challenge

[zoobyshoe]

Spoiler

Either I'm misunderstanding the question, or aren't there many solutions? (159, 478, 263)
and (259, 173, 468), for example, are both solutions they way I am reading the problem.

Spoiler

You are correct! I've re-written the problem to reflect the fact there is more than only one right answer.

 

[zoobyshoe]

Spoiler

Square = 6, Triangle = 3, Circle = 2

Spoiler

Correct!

 

[drizzle]

The tennis balls:

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1

 

[jhae2.718]

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

Take your shoe off, put the egg inside, and drop it four feet.

 

[zoobyshoe]

You bet someone you can drop a raw egg 4 feet without it breaking.

You can fulfill this pretty easily without moving or catching the egg, or magic or special effects, by simply taking advantage of something you haven't promised.

 

[zoobyshoe]

Spoiler

Take your shoe off, put the egg inside, and drop it four feet.

Spoiler

Try it. If it works, I accept it as correct. Hehe.

 

[jhae2.718]

Egg drop:

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Drop an egg that's already broken?

 

[drizzle]

... define raw egg, Zshoe?

 

[zoobyshoe]

Egg drop:

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Drop an egg that's already broken?

Spoiler

Hmmm...no.

 

[zoobyshoe]

... define raw egg, Zshoe?

Uncooked in any way. You are claiming you can drop it 4 feet without the shell or even the yolk breaking.

 

[drizzle]

Uncooked in any way. You are claiming you can drop it 4 feet without the shell or even the yolk breaking.

Spoiler

drop it from 5 feet, and catch it with your hand before it touches the ground? :b

 

[consciousness]

Another solution for raw egg (I think is the one zooby was getting at) -

Spoiler

Lift the egg to more than four feet and drop it. The egg will break but it will fall 4 feet without breaking! Fulfilling all the parameters in the problem!

 

[zoobyshoe]

another solution for raw egg (i think is the one zooby was getting at) -

Spoiler

lift the egg to more than four feet and drop it. The egg will break but it will fall 4 feet without breaking! Fulfilling all the parameters in the problem!

Bingo!

 

[drizzle]

Well, that's technically my answer, even if my try to catch it failed, it already passed the four feet safely, right Zshoe?

 

[zoobyshoe]

Well, that's technically my answer, even if my try to catch it failed, it already passed the four feet safely, right Zshoe?

Enigman already suggested your answer, though.

 

[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-

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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:

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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.

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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.