Riddles

Tarakiwa

MathsManiac wrote: »

3. Just to be clear, let's make the reasonable definition that "going into the wood" means moving farther from the edge and "going out of the wood" means going closer to the edge. Now, can you think of how you might start walking into the wood, reach a point where you can't go any further in any direction without coming out of the wood and still not be as far into the wood as someone else is?

Are you seeing the wood in some sort of 3D shape - so although you are in the middle of the wood (at ground level) if you were to climb half way up a tree in the middle of the wood you would be in the centre of the 3D shape?? Is that it?

gabigeist

MathsManiac wrote: »

2. Present a reasonable scenario in a short paragraph that results in the last sentence in the paragraph using the word "and" five times in a row.

I just wrote a letter to Brian and Brian. I'll have to reprint it though as I forgot to put a space between Brian and and and and and Brian.

gabigeist

MathsManiac wrote: »

Two languagey ones:

1. Punctuate this so that it makes sense:

THAT THAT IS IS THAT THAT IS NOT IS NOT IS NOT IT SO IT IS

"That that is" is "that". "That" is not "is not it". So it is.
or
"That that is" = "that"
"that" =/= "is not it"
Therefore "that"= "is it"
"that that is" = "is it"
So it is

Just chancing my arm with that one really

MathsManiac

Tarakiwa wrote: »

Are you seeing the wood in some sort of 3D shape - so although you are in the middle of the wood (at ground level) if you were to climb half way up a tree in the middle of the wood you would be in the centre of the 3D shape?? Is that it?

No. I could equally well have called it a field. You can assume we're talking about a flat region of land.

MathsManiac

gabigeist wrote: »

I just wrote a letter to Brian and Brian. I'll have to reprint it though as I forgot to put a space between Brian and and and and and Brian.

Same idea as the way I heard it, so I guess we can call that a right answer. Here's more or less how I heard it:

Mario ordered a sign for his chip-shop. The signwriter sent him a mock-up before starting it, but Mario wasn't quite happy with the spacing of the words, so he rang the guy and said: "I'd like a bit more space between Fish and and and and and Chips."

gabigeist

MathsManiac wrote: »

Same idea as the way I heard it [/spoiler]

Yeah it seems to have happened to a lot of us. Fair play to Mario for picking up on it so early.

Is the walk-into-woods-question

a case of a misshapen woods? e.g. circular woods with a large off-centre oval missing from the middle. Lots of other shapes would do I think

MathsManiac

gabigeist wrote: »

Is the walk-into-woods-question

a case of a misshapen woods? e.g. circular woods with a large off-centre oval missing from the middle. Lots of other shapes would do I think

Not the particular shape I had in mind, but yes, lots of shapes would do. Simplest, I think, is a large circle and a small circle joined at a narrow neck. When you're in the middle of the small circle, any direction brings you closer to the edge, yet someone in the middle of the large circle is farther in than you.

MathsManiac

Any more takers on number 1? None of the guesses so far are especially close. (BTW, I got it from an English teacher when I was in school years ago; he was pointing out the importance of punctuation!)

HoldStady

Sorry I don't know how to do spoilers or anything. The first bit seems okay but lost it at the end!


THAT THAT IS IS THAT THAT IS NOT IS NOT IS NOT IT SO IT IS

That, that is, is. That that is not, is not. is not it so it is.

MathsManiac

HoldStady wrote: »

Sorry I don't know how to do spoilers or anything. The first bit seems okay but lost it at the end!


THAT THAT IS IS THAT THAT IS NOT IS NOT IS NOT IT SO IT IS

That, that is, is. That that is not, is not. is not it so it is.

Well, I'd drop the first comma, but you might get away with it! As for the last bit:

Is not it so? It is.

Or you might prefer to put in quotation marks to make it a dialogue:

"That that is, is. That that is not, is not. Is not it so?"
"It is."

A really deep philosophical observation, as I'm sure you'll agree!

KnifeWRENCH

A maths lecturer gave us this one today:

A rich woman died and left her entire fortune of $10,000,000 to be divided equally between a number of lion tamers.
How much did each lion tamer receive?

molly_dolly

I am used to bat with, yet I never get a
hit. I am near a ball, yet it is never

thrown. What am I?

elmolesto

I'd say eyelashes

me-skywalker

MB74 wrote: »

Okay, it's an old one but there is an actual answer to this one....

Which came first, the chicken of the egg?

well the egg came first... here's how... aprehistoric birdlike creature cross-bred with some other prehistoric birdlike creature and created the egg from which the first chicken was hatched.

simple!

elly21

Cathy has six pairs of black gloves and six pairs of brown gloves in her drawer. In complete darkness, how many gloves must she take from the drawer in order to be sure to get a pair that match? Think carefully!!

patrickc

elly21 wrote: »

Cathy has six pairs of black gloves and six pairs of brown gloves in her drawer. In complete darkness, how many gloves must she take from the drawer in order to be sure to get a pair that match? Think carefully!!

2

elmolesto

13

elly21

your right

dos30

patrickc wrote: »

2

3????

errlloyd

Sorry for bumping a 5 year old thread, but I have a riddle I came up with I wanted you guys to solve - just to gauge if it's too hard or too easy.

I have a job, it's never ending but has two ends, it's paid in dollars, but worked in gold and no matter what the weather I always have my coat ready.

What do I do?

Quality

errlloyd wrote: »

Sorry for bumping a 5 year old thread, but I have a riddle I came up with I wanted you guys to solve - just to gauge if it's too hard or too easy.

I have a job, it's never ending but has two ends, it's paid in dollars, but worked in gold and no matter what the weather I always have my coat ready.

What do I do?

Painting? Golden Gate Bridge?

errlloyd

Quality wrote: »

Painting? Golden Gate Bridge?

Nice. Too easy? Or did you have to think about it?

Quality

errlloyd wrote: »

Nice. Too easy? Or did you have to think about it?

easy enough,, but i had my weetabix this morning.:cool:

errlloyd

Quality wrote: »

easy enough,, but i had my weetabix this morning.:cool:

Last question, promise.

Did you know that random piece of trivia about people constantly painting the golden gate bridge beforehand? Obviously whether you do or not has a bearing on how easy you find it.

Quality

errlloyd wrote: »

Last question, promise.

Did you know that random piece of trivia about people constantly painting the golden gate bridge beforehand? Obviously whether you do or not has a bearing on how easy you find it.

Yes I was on the Golden Gate Bridge before.

However it isn't painted golden!

JoeB-

MathsManiac wrote: »

Not the particular shape I had in mind, but yes, lots of shapes would do. Simplest, I think, is a large circle and a small circle joined at a narrow neck. When you're in the middle of the small circle, any direction brings you closer to the edge, yet someone in the middle of the large circle is farther in than you.

I had come up with that solution myself but I'm not sure if it's correct. Well, I know for certain the described shape doesn't work, but a modified one might.

The reason the given solution doesn't work is that if you were in the middle of the small circle then you could move directly through the neck towards the center of the large circle... that would be bringing you further into the center of the wood, and that's not allowed.

MathsManiac

JoeBallantine wrote: »

I had come up with that solution myself but I'm not sure if it's correct. Well, I know for certain the described shape doesn't work, but a modified one might.

The reason the given solution doesn't work is that if you were in the middle of the small circle then you could move directly through the neck towards the center of the large circle... that would be bringing you further into the center of the wood, and that's not allowed.

That's incorrect. If you walk in the direction you specify, you are getting closer to the edge of the wood, which was the definition given for going out of the wood. (When you are close to the neck, you are very close to the edge of the wood, no matter what direction you are moving, so you are farther out of the wood than you were previously.)

JoeB-

I know what you're saying but I still don't agree.

The whole system of 'going in' and 'going out' doesn't work is all cases.

If there are two separated circular woods and they are connected by a long, narrow, winding neck then the whole concept of 'in', 'out' and moving closer to the center or further away doesn't really work, .. due to the long, narrow, winding neck connecting two otherwise separate circular woods.

So, .. when a person moves from the small circle, along the neck, .. they are neither moving in or out.. as they remain equidistant from the edges of the wood. But yes, .. when moving along the narrow neck they are closer to the edge then they would have been when in the center of the small circle, so it is correct I suppose to say that they must have moved 'outwards' in order to get closer to the edge.
(But in another valid sense they haven't moved outwards at all,.. in that they've remained in the center of the wood at all times, and it's only that the center of the wood itself has moved 'outwards')



If there are two circles, a small and a big, and these intersect with no neck then what I said originally is correct.. you can move from the center of the little circle and only move inwards if you head directly towards the center of the large circle. However, once the circles do not intersect and instead they must be connected by a neck, then all bets are off, and the definitions start to fail, .. especially if the neck is winding.



Edit. Now I'm not sure at all (even with two intersecting circles with no neck), .. but I don't think the definitions of 'in' and 'out' etc are robust enough to handle long winding necks.

MathsManiac

But it was precisely in order to remove any such ambiguity that a definition of "into" and "out of" was given in the first place. The system of 'going in' and 'going out' is precise and well defined in all cases.

That definition was that if you move in such a way that your distance to the closest point of the edge of the wood is increasing, then you are going into the wood, while if that distance is decreasing, you are going out of the wood. You might not like that definition, but it was given as part of the puzzle.

Another way of thinking about it is to imagine you have a circular "bubble", centred on you, and constantly as large as it can be, within the confines of the wood. If you move in such a way that your bubble can get bigger, you're going into the wood, while if you're moving in such a way that your bubble is forced to get smaller, you are moving out of the wood. (Of couse, if your bubble stays the same, you are neither moving into or out of the wood.)

Mellor

JoeBallantine wrote: »

I had come up with that solution myself but I'm not sure if it's correct. Well, I know for certain the described shape doesn't work, but a modified one might.

The reason the given solution doesn't work is that if you were in the middle of the small circle then you could move directly through the neck towards the center of the large circle... that would be bringing you further into the center of the wood, and that's not allowed.

That's incorrect.

When you leave the centre of the small circle, you are getting closer to the edge, when you reach the "neck" you could very well stop getting closer to the edge, but the fact remains that you closer then the opoint you started.

JoeBallantine wrote: »

If there are two separated circular woods and they are connected by a long, narrow, winding neck then the whole concept of 'in', 'out' and moving closer to the center or further away doesn't really work, .. due to the long, narrow, winding neck connecting two otherwise separate circular woods.

It does work.
You are confusing the centre of the woods with the centre of the neck

So, .. when a person moves from the small circle, along the neck, .. they are neither moving in or out.. as they remain equidistant from the edges of the wood.

No they dont????
The edge might the same distance in both directions at any point along this path (from centre to centre along neck), but its not the same distance the entire time.

But yes, .. when moving along the narrow neck they are closer to the edge then they would have been when in the center of the small circle, so it is correct I suppose to say that they must have moved 'outwards' in order to get closer to the edge.

Exactly, therefore its wrong.

(But in another valid sense they haven't moved outwards at all,.. in that they've remained in the center of the wood at all times, and it's only that the center of the wood itself has moved 'outwards')

Thats not valid at all. The centre hasn't moved, the centre of the neck isn't in the centre of the woods.

If there are two circles, a small and a big, and these intersect with no neck then what I said originally is correct.. you can move from the center of the little circle and only move inwards if you head directly towards the center of the large circle.

Thats not true either.

Firstly, when you leave the centre of the smaller circle, you are getting closer to the edge you reach the area when the circles "overlap".



Even if the centre of the small circle is right on the bigger circle, and there is no travel before you get to the overlap it. It still isn't true. You'll initially get closer to the edge until you get to the point halfway between where the two circles intersect.

Also, the centre of the small circle isn't the centre of the woods either.

However, once the circles do not intersect and instead they must be connected by a neck, then all bets are off, and the definitions start to fail, .. especially if the neck is winding.

Not true.
For the same reasons as above.

JoeB-

I agree that my original point is wrong.


Some observations.
The 'center' isn't referred to in the original description.
Instead, distances from the edge are mentioned. So the center is the furthest point from the edge. There can be several centers,.. each then being a local center if you like.

Moving from one local center to another does always require 'going out' of the wood... by definition.
(in other words, if it was possible to move from a local center further into the wood then the center would not have been the center at all !!!)



The center doesn't need to be a single point. It could be a line. In which case, it'd be possible for a walker to be entirely within the wood, and to walk continuously but yet never go further into the wood, or out of the wood.



edited to add:
Original description
3. Just to be clear, let's make the reasonable definition that "going into the wood" means moving farther from the edge and "going out of the wood" means going closer to the edge. Now, can you think of how you might start walking into the wood, reach a point where you can't go any further in any direction without coming out of the wood and still not be as far into the wood as someone else is?

Mellor

JoeBallantine wrote: »

Some observations.
The 'center' isn't referred to in the original description.
Instead, distances from the edge are mentioned. So the center is the furthest point from the edge. There can be several centers,.. each then being a local center if you like.

I was understand that the centre was the answer, not the question.

Are we talking about different questions?


Moving from one local center to another does always require 'going out' of the wood... by definition.
(in other words, if it was possible to move from a local center further into the wood then the center would not have been the center at all !!!)

The center doesn't need to be a single point. It could be a line. In which case, it'd be possible for a walker to be entirely within the wood, and to walk continuously but yet never go further into the wood, or out of the wood.

As in a rectangular wood.

jack747

I've got one if a tree fell in a forest did anyone hear it. lol..rofl

JoeB-

Mellor wrote: »

....
As in a rectangular wood.

Does a rectangular wood have a center that's a single point?, or a line?

I'd have thought that the rectangle center is a single point.

I'm still not convinced that the whole wood thing works,.. and it might well revolve around whether or not the center of a rectangle is a line or a point.


The reason I think that the center of a rectangular wood is a point is that if we allow it to be a line, .. then when one stands on the endpoint of the line they could move towards the midpoint of the line,.. and by so doing they are moving further away from the (short) edge of the rectangle while remaining at a constant distance from the long side. Hence they would appear to be 'going into' the wood.

So a rectangular wood only has a point as the center, similar to a circular wood, or a square wood.



It's possible to have a center represented by a line, and the line need not have an end either.

Consider a circular wood. Now remove a small circular section from the exact center of the wood, leaving a ring. This ring shaped wood has a center in the shape of a circle.

1100010110

Would a spiral path approaching the centre of a circular wood not work? And to the mathematicks out there, is that an infinite distance?

Mellor

JoeBallantine wrote: »

Does a rectangular wood have a center that's a single point?, or a line?

Depend on how you (or the question) define centre.
Centre of area. It's a point.
Distance from the edge. It's a line.
Distance from all edges is prob a point.

I'd have thought that the rectangle center is a single point.

I would too. In normal circumstances.
I'm still not convinced that the whole wood thing works,.. and it might well revolve around whether or not the center of a rectangle is a line or a point.

The reason I think that the center of a rectangular wood is a point is that if we allow it to be a line, .. then when one stands on the endpoint of the line they could move towards the midpoint of the line,.. and by so doing they are moving further away from the (short) edge of the rectangle while remaining at a constant distance from the long side. Hence they would appear to be 'going into' the wood.

But they aren't going any further into the wood, the distance to get out is not increasing.

Consider a circular wood. Now remove a small circular section from the exact center of the wood, leaving a ring. This ring shaped wood has a center in the shape of a circle.

Distance from edge is a circle
Centre of area is a point in the centre of the ring.

1100010110 wrote: »

Would a spiral path approaching the centre of a circular wood not work?

I what what would that work?
I think people are talking about different questions.

And to the mathematicks out there, is that an infinite distance?

No. Why would it be.

1100010110

Mellor wrote: »

I what what would that work?
I think people are talking about different questions.

How far into the woods can you walk? Was that not the question?

Mellor wrote: »

No. Why would it be.

f(x) y=square root x?

1100010110

Mellor wrote: »

I what what would that work?

What? Wot wot? 5.01am you say?

Mellor

1100010110 wrote: »

How far into the woods can you walk? Was that not the question?

Yes
Your suggestion is a long route to the centre. But it gets no further in. Walking around in circles also a long route, but doesn't get far in.

f(x) y=square root x?

Each revolution of the spiral gets shorter so the function needs to approach zero.

Eg
1 +1/2+1/2...to infinite = 2

1100010110 wrote: »

What? Wot wot? 5.01am you say?

2pm actually, so can't even use the time as an excuse

1100010110

Surely a spiral path from any point on the edge of a circular woods approaching the centre is constantly getting further from the edge?
And so the distance travelled into the woods is constantly increasing, and if it approaches but never reaches the centre then it is an infinite distance?

I think I'm just taking the "how far can you travel into" part of the puzzle and trying to find that,
which would be an infinite distance on a spiral path into a circular wood which approaches but never reaches the centre.

My bad on the time, was just a bit confussed and presumed without checking the available facts.

JoeB-

Mellor wrote: »

Joe Ballantine said 'Consider a circular wood. Now remove a small circular section from the exact center of the wood, leaving a ring. This ring shaped wood has a center in the shape of a circle.'

Distance from edge is a circle
Centre of area is a point in the centre of the ring.

This is the reason I brought this up. The center of the wood can hardly be outside the wood, as it would be if it was in the exact center of a doughnut shaped wood. So the 'center' that fits the description given must be the circle. (i.e equal distance from edges)

The original statement mentioned going into and going out of the wood, but it didn't define the center itself.
We have since half defined the center to be a point where you cannot go further into the wood, without first going out of the wood. (There can be several centers)





The spiral path is new to me.

Can a path of infinite length be drawn in a finite circle? Is this a non-overlapping path?

A toilet roll cannot be infinite in length. (for a given thickness of roll and paper) as the paper itself has thickness. A thinner paper would take up less room.

So the length of a spiral path into the wood would depend on the thickness of the path, and whether it can be overlapping or not. Overlapping is likely not allowed. A path of zero width is not possible. So an infinite path is not possible.






Incidentally, can anyone give a formula for the thickness (diameter) of a toilet roll, given the length of the paper R say, and the thickness of the paper, T say, and the diameter of the paper core, say D. Can the diameter of the resulting roll be given in terms of R,T and C?


Say R = 50 meters = 50,000 mm
T = 1mm
C = 40mm

Final thickness of roll = ???

I think this is hard enough. I can approximate an answer handily enough, with one assumption made. I may need to use a spreadsheet to help.

To get an exact answer is tougher,
(no answer given here, but some observations)

especially if it's considered that the diameter of the roll is constantly increasing, requiring calculus to be used I'd imagine.

Constantly increasing in diameter as opposed to only increasing in a single step once per revolution, in which case an arithmetic progression rather than calculus might be useful.