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Maths Challenge


Skydie
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Recently many players have been arguing about Mathematics in these forums. Many have accused others of being inferior in the art of Mathematics and added emotion language in. Things are getting tense, I understand...

 

That is why I have setup Maths Challenge.

 

Anyone who argues anything about Maths should show they are worth their substance and have a challenge here.

 

Challenge layout:

Person 1 challenges Person 2

Person 1 comes up with 3 questions (which they can answer) to challenge Person 2

Person 2 completes them

Person 2 comes up with 3 questions (which they can answer) to challenge Person 1

Person 1 completes them

Done.

 

 

Current challenges:

 

Mus challenging Midknight.

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Math/Logic problem to all that think they are at least half as smart as I am:

 

Assuming Pinocchio's nose grows at a certain length after each time that he tells a lie, and shrinks by that same amount every time he admits the truth (it stops after reaching original length pre-lies), what is his nose length going to be after a few seconds of him saying "my nose is growing?"

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This wouldn't be a problem similar to the original Pinnochi paradox would it? Like say, the nose would not grow at first, so the statement that Pinnochio's nose is growing, as in is growing at this very moment, is false. But after a second or so, his nose then grows, fulfilling the condition that Pinnochio's nose grows when he tells a lie.

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My challenges to whoever will accept them.

 

1) Imagine you have a standard NBA basketball with a rope tightly wound around its equator. Now imagine you have a rope similarly wrapped around the equator of the Earth. You have to add enough length to the ropes so that they ring the respective spheres one foot higher (ie, the ropes are floating in a circle one foot above the surface of the ball/Earth). How much more do you have to add to the rope around the Earth than to the rope around the ball?

 

2) How many grooves does a standard 12" Gramophone (vinyl) record have?

 

3) You have a 12" Gramophone record with a 3" label. Presuming that it plays from exactly 6" out and ends 1.5" from the center, how far has the needle moved in playing the entire record?

 

Bonus) A man is 1km from a tree. He is riding a Segway that travels at 20km/h. To reach the tree, he must first travel half the distance. From there, he must travel half the remaining distance. Each time he travels half the distance, he must then travel half the remaining distance. You can halve the remaining distance infinitely. Does he ever reach the tree and, if so, how long does it take?

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This wouldn't be a problem similar to the original Pinnochi paradox would it? Like say, the nose would not grow at first, so the statement that Pinnochio's nose is growing, as in is growing at this very moment, is false. But after a second or so, his nose then grows, fulfilling the condition that Pinnochio's nose grows when he tells a lie.

 

Damn it, someone else thought of it first!?!?!??! flob, we live in an age where nothing is left to discover....... you have no idea how many things I thought I created or discovered, and then found out that someone beat me to the punch. Why, oh why couldn't I have lived in Ancient Greece, where society was more or less acceptably developed, yet most things were blissfully uninvented, and I wouldn't have to find out the hard way that someone else came up with several theological, philosophical, or practical concepts I thought to be mine own...........

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My challenges to whoever will accept them.

 

1) Imagine you have a standard NBA basketball with a rope tightly wound around its equator. Now imagine you have a rope similarly wrapped around the equator of the Earth. You have to add enough length to the ropes so that they ring the respective spheres one foot higher (ie, the ropes are floating in a circle one foot above the surface of the ball/Earth). How much more do you have to add to the rope around the Earth than to the rope around the ball?

 

2) How many grooves does a standard 12" Gramophone (vinyl) record have?

 

3) You have a 12" Gramophone record with a 3" label. Presuming that it plays from exactly 6" out and ends 1.5" from the center, how far has the needle moved in playing the entire record?

I quit because of lack of metric system.

Bonus) A man is 1km from a tree. He is riding a Segway that travels at 20km/h. To reach the tree, he must first travel half the distance. From there, he must travel half the remaining distance. Each time he travels half the distance, he must then travel half the remaining distance. You can halve the remaining distance infinitely. Does he ever reach the tree and, if so, how long does it take?

Eh, 3 minutes I guess. Even if he has to travel half the remaining distance each time, I assume he travels the distance at a constant speed of 20km/h. So in the end, his average speed throughout the journey is simply 20km/h.

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My challenges to whoever will accept them.

 

1) Imagine you have a standard NBA basketball with a rope tightly wound around its equator. Now imagine you have a rope similarly wrapped around the equator of the Earth. You have to add enough length to the ropes so that they ring the respective spheres one foot higher (ie, the ropes are floating in a circle one foot above the surface of the ball/Earth). How much more do you have to add to the rope around the Earth than to the rope around the ball?

 

2) How many grooves does a standard 12" Gramophone (vinyl) record have?

 

3) You have a 12" Gramophone record with a 3" label. Presuming that it plays from exactly 6" out and ends 1.5" from the center, how far has the needle moved in playing the entire record?

 

Bonus) A man is 1km from a tree. He is riding a Segway that travels at 20km/h. To reach the tree, he must first travel half the distance. From there, he must travel half the remaining distance. Each time he travels half the distance, he must then travel half the remaining distance. You can halve the remaining distance infinitely. Does he ever reach the tree and, if so, how long does it take?

 

 

Imma not sure about basketballs, or Gramaphone records, I usually tend to avoid both of these in my day-to-day life, but I'll take a crack at the bonus.

 

1: Seems very much like the Ancient Greece problem of Hercules and Tortise, except the tree is not running away, thus making all the divisions a bit redundant......

 

 

2: Why does he beat about the bush with all these half distances and not just keep going? Seems lot easier, especially since he'd probably have to stop to make calculations and measurements to get everything exactly right to all the decimal places..... not to mention calculate his speed to make up for the stops, unless he can make the appropriate measurements and calculations on the go, in which case I solute him, and hope that he finds what he's looking for once he gets to the tree.

 

 

3 Ok, first at a speed of 20 km/h it takes 3 minutes to cross 1 km, therefore 1.5 minute to cross 0.5

 

4. I'm assuming that we have to use the geometric series formula of Sinfinite = T1/ (1 - r)

 

so that would look like: Sinfinite = 1.5/ (1-0.5) =

 

1.5/0.5 = 3 minutes, which means that I retardedly overthought your problem, which I guess was the desired effect.

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