Can You Solve This
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For all the Mathematicians OUT THERE
Five dots are arranged in space so that no more than three at a time can have a single flat surface pass through them. If each group of three dots has a flat surface pass through it and extend an infinite distance in every direction, what is the maximum number of different lines at which these surfaces may intersect one another?
Don't worry, even from here I can clearly hear you say, "Huh?"
:)
"The most beautiful thing we can experience is the mysterious" -Albert Einstein -- modified at 13:25 Monday 24th October, 2005
Two. :suss: -- LuisR
Luis Alonso Ramos Intelectix - Chihuahua, Mexico Not much here: My CP Blog!
The amount of sleep the average person needs is five more minutes. -- Vikram A Punathambekar, Aug. 11, 2005
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Two. :suss: -- LuisR
Luis Alonso Ramos Intelectix - Chihuahua, Mexico Not much here: My CP Blog!
The amount of sleep the average person needs is five more minutes. -- Vikram A Punathambekar, Aug. 11, 2005
Ok, I accept it, I have no clue!! It's just a wild guess! :-D -- LuisR
Luis Alonso Ramos Intelectix - Chihuahua, Mexico Not much here: My CP Blog!
The amount of sleep the average person needs is five more minutes. -- Vikram A Punathambekar, Aug. 11, 2005
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For all the Mathematicians OUT THERE
Five dots are arranged in space so that no more than three at a time can have a single flat surface pass through them. If each group of three dots has a flat surface pass through it and extend an infinite distance in every direction, what is the maximum number of different lines at which these surfaces may intersect one another?
Don't worry, even from here I can clearly hear you say, "Huh?"
:)
"The most beautiful thing we can experience is the mysterious" -Albert Einstein -- modified at 13:25 Monday 24th October, 2005
Huh? Ok, let me try it. So if you have 5 dots to be arranged by 3 to define planes you'd have: combination of 5 by 3= (5!) / ( (5-3)! * 3!) = 10 planes Now, for 1 plane you'd have 0 lines. For each extra plane you add you would have the existing lines plus a number of lines equal to the previously existing number of planes (since the new plane will intercept the existing just once). So:
planes lines
1 0
2 1
3 3
4 6
5 10
6 15
7 21
8 28
9 36
10 45or, as a formula:
lines( 1 )=0 if planes=1
lines( planes )= lines( planes-1)+ planes-1 if planes > 1Makes sense? :confused: Rui A. Rebelo I don't smoke, don't gamble, don't sniff, don't drink and don't womanize. My only defect is that I lie just a little bit, sometimes. Tim Maia (brazilian pop singer) -- modified at 13:46 Monday 24th October, 2005
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For all the Mathematicians OUT THERE
Five dots are arranged in space so that no more than three at a time can have a single flat surface pass through them. If each group of three dots has a flat surface pass through it and extend an infinite distance in every direction, what is the maximum number of different lines at which these surfaces may intersect one another?
Don't worry, even from here I can clearly hear you say, "Huh?"
:)
"The most beautiful thing we can experience is the mysterious" -Albert Einstein -- modified at 13:25 Monday 24th October, 2005
-
For all the Mathematicians OUT THERE
Five dots are arranged in space so that no more than three at a time can have a single flat surface pass through them. If each group of three dots has a flat surface pass through it and extend an infinite distance in every direction, what is the maximum number of different lines at which these surfaces may intersect one another?
Don't worry, even from here I can clearly hear you say, "Huh?"
:)
"The most beautiful thing we can experience is the mysterious" -Albert Einstein -- modified at 13:25 Monday 24th October, 2005
Well, the whole 5 dots thing is a red herring, since we can only have three dots with planes passing between them. So lets narrow it down to three by setting the extra two dots off in the distance (such that a plane we set down won't pass between them or the other dots). Then we've got three dots, and there are two spaces between them, each allowing one flat surface. So we lay down our flat surfaces and dots like so:
\ /
. \ . / .
\ /
\ /
\/
/\
/ \Then we've got two planes intersecting at one line. (Think of this as a top down view, and the "line" at which they intersect is in the middle of the X, extending through your monitor). Am I right?
Picture a huge catholic cathedral. In it there's many people, including a gregorian monk choir. You know, those who sing beautifully. Then they start singing, in latin, as they always do: "Ad hominem..." -Jörgen Sigvardsson
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Huh? Ok, let me try it. So if you have 5 dots to be arranged by 3 to define planes you'd have: combination of 5 by 3= (5!) / ( (5-3)! * 3!) = 10 planes Now, for 1 plane you'd have 0 lines. For each extra plane you add you would have the existing lines plus a number of lines equal to the previously existing number of planes (since the new plane will intercept the existing just once). So:
planes lines
1 0
2 1
3 3
4 6
5 10
6 15
7 21
8 28
9 36
10 45or, as a formula:
lines( 1 )=0 if planes=1
lines( planes )= lines( planes-1)+ planes-1 if planes > 1Makes sense? :confused: Rui A. Rebelo I don't smoke, don't gamble, don't sniff, don't drink and don't womanize. My only defect is that I lie just a little bit, sometimes. Tim Maia (brazilian pop singer) -- modified at 13:46 Monday 24th October, 2005
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Well, the whole 5 dots thing is a red herring, since we can only have three dots with planes passing between them. So lets narrow it down to three by setting the extra two dots off in the distance (such that a plane we set down won't pass between them or the other dots). Then we've got three dots, and there are two spaces between them, each allowing one flat surface. So we lay down our flat surfaces and dots like so:
\ /
. \ . / .
\ /
\ /
\/
/\
/ \Then we've got two planes intersecting at one line. (Think of this as a top down view, and the "line" at which they intersect is in the middle of the X, extending through your monitor). Am I right?
Picture a huge catholic cathedral. In it there's many people, including a gregorian monk choir. You know, those who sing beautifully. Then they start singing, in latin, as they always do: "Ad hominem..." -Jörgen Sigvardsson
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Well, the whole 5 dots thing is a red herring, since we can only have three dots with planes passing between them. So lets narrow it down to three by setting the extra two dots off in the distance (such that a plane we set down won't pass between them or the other dots). Then we've got three dots, and there are two spaces between them, each allowing one flat surface. So we lay down our flat surfaces and dots like so:
\ /
. \ . / .
\ /
\ /
\/
/\
/ \Then we've got two planes intersecting at one line. (Think of this as a top down view, and the "line" at which they intersect is in the middle of the X, extending through your monitor). Am I right?
Picture a huge catholic cathedral. In it there's many people, including a gregorian monk choir. You know, those who sing beautifully. Then they start singing, in latin, as they always do: "Ad hominem..." -Jörgen Sigvardsson
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I don't know. It makes sense to me, but I suspect there might be something I didn't notice.:confused::~ Rui A. Rebelo I don't smoke, don't gamble, don't sniff, don't drink and don't womanize. My only defect is that I lie just a little bit, sometimes. Tim Maia (brazilian pop singer)
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10 Bags with 100 coins each Each coin is 10 gms in 9 bags Each coin is 9 gms in one bag (you dont know which ONE bag) You have a weiging machine which gives you the exact weight
You can use the weighing machine EXACTLY ONCE
How will you fnd which bag has coins of 9 gms
You have time till the evening Ask me if any doubt about the question
[DON"T SEE THE ANSWERS BELOW IF YOU SOLVED IT BY YOURSELF DO TELL BE HOW MUCH TIME IT TOOK] "Not everything that counts can be counted..." -Albert Einstein -- modified at 13:03 Monday 24th October, 2005
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What do you think ? :sigh: "Not everything that counts can be counted..." -Albert Einstein
Quartz... wrote:
What do you think ?
I think that I'm right. I don't see a way in which I could position the points and planes in a way that would allow me to get a different answer.
Picture a huge catholic cathedral. In it there's many people, including a gregorian monk choir. You know, those who sing beautifully. Then they start singing, in latin, as they always do: "Ad hominem..." -Jörgen Sigvardsson
-
For all the Mathematicians OUT THERE
Five dots are arranged in space so that no more than three at a time can have a single flat surface pass through them. If each group of three dots has a flat surface pass through it and extend an infinite distance in every direction, what is the maximum number of different lines at which these surfaces may intersect one another?
Don't worry, even from here I can clearly hear you say, "Huh?"
:)
"The most beautiful thing we can experience is the mysterious" -Albert Einstein -- modified at 13:25 Monday 24th October, 2005
Quartz... wrote:
Five dots are arranged in space so that no more than three at a time can have a single flat surface pass through them.
3D space or 4D or n Dimensional mathematics? ;P (yes I am heartless at times, but it really does make a difference) _________________________ Asu no koto o ieba, tenjo de nezumi ga warau. Talk about things of tomorrow and the mice in the ceiling laugh. (Japanese Proverb)
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Quartz... wrote:
What do you think ?
I think that I'm right. I don't see a way in which I could position the points and planes in a way that would allow me to get a different answer.
Picture a huge catholic cathedral. In it there's many people, including a gregorian monk choir. You know, those who sing beautifully. Then they start singing, in latin, as they always do: "Ad hominem..." -Jörgen Sigvardsson
-
Quartz... wrote:
Five dots are arranged in space so that no more than three at a time can have a single flat surface pass through them.
3D space or 4D or n Dimensional mathematics? ;P (yes I am heartless at times, but it really does make a difference) _________________________ Asu no koto o ieba, tenjo de nezumi ga warau. Talk about things of tomorrow and the mice in the ceiling laugh. (Japanese Proverb)
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Hey. Do you remember the Fat Point Teorem from the school? Teorem: Throught a point can pass infinite lines, and much more lines the fatter the point is. Take a pen and paper. It's easy to demostrate it.
Fat Point theorem wow, never heard about that thanks for the illumination. but please don't bother yourself with the FAT POINTS for the above problem we have got 5 simple little points here. "Not everything that counts can be counted..." -Albert Einstein
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Ok, I accept it, I have no clue!! It's just a wild guess! :-D -- LuisR
Luis Alonso Ramos Intelectix - Chihuahua, Mexico Not much here: My CP Blog!
The amount of sleep the average person needs is five more minutes. -- Vikram A Punathambekar, Aug. 11, 2005
Ok, I accept it, I have no clue!! It's just a wild guess!
I knew it by the speed in which you answered :) anyway try somthing The most difficult problems sometimes have the most simple solutions... "Not everything that counts can be counted..." -Albert Einstein
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For all the Mathematicians OUT THERE
Five dots are arranged in space so that no more than three at a time can have a single flat surface pass through them. If each group of three dots has a flat surface pass through it and extend an infinite distance in every direction, what is the maximum number of different lines at which these surfaces may intersect one another?
Don't worry, even from here I can clearly hear you say, "Huh?"
:)
"The most beautiful thing we can experience is the mysterious" -Albert Einstein -- modified at 13:25 Monday 24th October, 2005
The five dots are not a red herring... however my headache means I am not the best to predict the results this evening. Consider this: Arrange three pens or pencils on a table, or tooth picks if you prefer in a triangle shape:
/\
/ \This represents three of your points and one plane. Now hold a single pen/pencil or toothpic over the top of the triangle suspended in mid air. Imagine building up a connecting object by connecting all points to all points. The result is an object with six sides, but a very odd shape.
/\
/ \Each of those planes connects once at your object, with I believe 9 lines where the planes cross. However the planes are infinately long. So the question is, does any of those planes cross anywhere else other than at the shape in the center. That is where my headache cannot go beyond today. _________________________ Asu no koto o ieba, tenjo de nezumi ga warau. Talk about things of tomorrow and the mice in the ceiling laugh. (Japanese Proverb)
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Wow i am excited a new star in the horizon :) Lets Do it For 3D first....... "Not everything that counts can be counted..." -Albert Einstein
Quartz... wrote:
Wow i am excited a new star in the horizon
Not really, I am lousy at math, but I could easily write a program to display it. N dimensional math just makes for more interesting shapes. _________________________ Asu no koto o ieba, tenjo de nezumi ga warau. Talk about things of tomorrow and the mice in the ceiling laugh. (Japanese Proverb)