[ARCHIVED THREAD] - A Real Actual Math Problem (Page 1 of 2)
Posted: 3/8/2015 6:23:59 PM EDT
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Imagine there is a large cube formed by gluing together 125 smaller wooden cubes. A termite starts at the center cube of any one of the faces of the large cube, burrowing through each smaller cube exactly once and ending at the center. He can only travel parallel to the sides of the large cube. (he can't travel diagonally). Is this possible?
You must justify your answer to be correct. Eta: All of the necessary information is in the original post; to clarify: He has to burrow through all 124 cubes exactly once. He starts on any "outside" cube that is in the center of one of the faces of the larger cube. He must end at the center cube of the larger amalgam. He can only make 90k degree turns. {k=1,2,3...} In other words, he can't travel in diagonals relative to the larger cubes faces. |
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Quoted: Imagine there is a large cube formed by gluing together 125 smaller wooden cubes. A termite starts at the center cube of any one of the faces of the large cube, burrowing through each smaller cube exactly once and ending at the center. He can only travel parallel to the sides of the large cube. (he can't travel diagonally). Is this possible? You must justify your answer to be correct. Because you just said he did it before asking if it was possible, so my answer is yes  |
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Since there is no restriction on backtracking through already created tunnels,, sure, this ought to be pretty simple.
Edit to add the query at the time of my reply: Imagine there is a large cube formed by gluing together 125 smaller wooden cubes. A termite starts at the center cube of any one of the faces of the large cube, burrowing through each smaller cube exactly once and ending at the center. He can only travel parallel to the sides of the large cube. (he can't travel diagonally). Is this possible? You must justify your answer to be correct. Edit further: burrowing is not walking... |
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Quoted: Imagine there is a large cube formed by gluing together 125 smaller wooden cubes. A termite starts at the center cube of any one of the faces of the large cube, burrowing through each smaller cube exactly once and ending at the center. He can only travel parallel to the sides of the large cube. (he can't travel diagonally). Is this possible? No. You must justify your answer to be correct. It's a soldier termite. |
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What is the question? I only see statements... I don't see math. Usually math problems have some numbers then symbols then more numbers, maybe more symbols, numbers, squiggly lines, numbers, over a line with lots of numbers and symbols with parentheses around numbers, and a place to show your work. This is not that. There are very few termites in math problems. And fewer math problems with termites. |
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Imagine there is a large cube formed by gluing together 125 smaller wooden cubes. A termite starts at the center cube of any one of the faces of the large cube, burrowing through each smaller cube exactly once and ending at the center. He can only travel parallel to the sides of the large cube. (he can't travel diagonally). Is this possible? You must justify your answer to be correct. Eta: All of the necessary information is in the original post; to clarify: He has to burrow through all 124 cubes exactly once. He starts on any "outside" cube that is in the center of one of the faces of the larger cube. He must end at the center cube of the larger amalgam. He can only make 90k degree turns. {k=1,2,3...} In other words, he can't travel in diagonals relative to the larger cubes faces. Stop moving the goalposts If you can't clearly explain the problem, stop trying |
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Stop moving the goalposts If you can't clearly explain the problem, stop trying Quoted:
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Imagine there is a large cube formed by gluing together 125 smaller wooden cubes. A termite starts at the center cube of any one of the faces of the large cube, burrowing through each smaller cube exactly once and ending at the center. He can only travel parallel to the sides of the large cube. (he can't travel diagonally). Is this possible? You must justify your answer to be correct. Eta: All of the necessary information is in the original post; to clarify: He has to burrow through all 124 cubes exactly once. He starts on any "outside" cube that is in the center of one of the faces of the larger cube. He must end at the center cube of the larger amalgam. He can only make 90k degree turns. {k=1,2,3...} In other words, he can't travel in diagonals relative to the larger cubes faces. Stop moving the goalposts If you can't clearly explain the problem, stop trying I'm not moving the goalpost. I'm expanding dense writing to aid people who aren't used to actually reading every word in a sentence. |
Easy.
http://imgur.com/SJsrSPZ (Starts at the center of the outside face, moves through all the squares to the upper right corner, enters the next slice at the upper right corner and moves through all the squares to the lower leg corner, enters the center slice ay the lower left corner and moves through all the squares except the center one, enters the 4th slice at the square 1 right of center amd moves through all of the squares except the center one, enters the back face in the lower left corner and moves through all the squares, ending on the center square of the back face. Then proceed back to the center of the 4th slice, and finally back to the center of the middle slice to complete) If you're looking for a mathematical proof of this, then sorry. (Not sure if I did something wrong with the picture) |
If I understood it appropriately, this is how it could work. Red dots are entering/leaving a "layer", green line is path. Also my termite is drunk. I'm way too far out of college to offer a mathematical proof, but I remember a lot of similar questions so I'm sure it isn't hard. |
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Easy. http://imgur.com/SJsrSPZ http://imgur.com/SJsrSPZ (Starts at the center of the outside face, moves through all the squares to the upper right corner, enters the next slice at the upper right corner and moves through all the squares to the lower leg corner, enters the center slice ay the lower left corner and moves through all the squares except the center one, enters the 4th slice at the square 1 right of center amd moves through all of the squares except the center one, enters the back face in the lower left corner and moves through all the squares, ending on the center square of the back face. Then proceed back to the center of the 4th slice, and finally back to the center of the middle slice to complete) If you're looking for a mathematical proof of this, then sorry. (Not sure if I did something wrong with the picture) That's correct. 
At least, that's one of the ways to do it. |
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That's correct.
At least, that's one of the ways to do it. Quoted:
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Easy. http://imgur.com/SJsrSPZ http://imgur.com/SJsrSPZ (Starts at the center of the outside face, moves through all the squares to the upper right corner, enters the next slice at the upper right corner and moves through all the squares to the lower leg corner, enters the center slice ay the lower left corner and moves through all the squares except the center one, enters the 4th slice at the square 1 right of center amd moves through all of the squares except the center one, enters the back face in the lower left corner and moves through all the squares, ending on the center square of the back face. Then proceed back to the center of the 4th slice, and finally back to the center of the middle slice to complete) If you're looking for a mathematical proof of this, then sorry. (Not sure if I did something wrong with the picture) That's correct.
At least, that's one of the ways to do it. Wouldn't his last layer have to be done in a closing spiral to end up at the center? ETA: I vaguely remember something called a Hamiltonian (in 3d vector calc, maybe?) but that was many many beers ago. |
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Quoted: http://i.imgur.com/yaMBBGd.jpg If I understood it appropriately, this is how it could work. Red dots are entering/leaving a "layer", green line is path. Also my termite is drunk. I'm way too far out of college to offer a mathematical proof, but I remember a lot of similar questions so I'm sure it isn't hard. Shame on you termite! |
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Invalid starting point. If I remember correctly, 342 sub v means it should have least one valid Hamiltonian circuit from any given point on the outer face. It's obviously an NP-complete problem and I'm not even going to try it on my laptop. Eta: yup http://akcejournal.org/contents/vol4no3/vol4no3-3.pdf |
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and who really cares? Quoted:
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How did the termite get into the centre of the cube ? and who really cares? Well if it's a problem then all known evidence should be put forth to solve said problem. Other than that it's just trivial fodder when somebody questions the motive and it cannot be put in to a rational outcome . Termite much bro ? |
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Invalid starting point. If I remember correctly, 342 sub v means it should have least one valid Hamiltonian circuit from any given point on the outer face. It's obviously an NP-complete problem and I'm not even going to try it on my laptop. Eta: yup http://akcejournal.org/contents/vol4no3/vol4no3-3.pdf Quoted:
Invalid starting point. If I remember correctly, 342 sub v means it should have least one valid Hamiltonian circuit from any given point on the outer face. It's obviously an NP-complete problem and I'm not even going to try it on my laptop. Eta: yup http://akcejournal.org/contents/vol4no3/vol4no3-3.pdf 
(edited to alter the perspective so that path lines are a little easier to see) |
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http://s15.postimg.org/drr8j0swb/termite_path.jpg (edited to alter the perspective so that path lines are a little easier to see) Quoted:
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Invalid starting point. If I remember correctly, 342 sub v means it should have least one valid Hamiltonian circuit from any given point on the outer face. It's obviously an NP-complete problem and I'm not even going to try it on my laptop. Eta: yup http://akcejournal.org/contents/vol4no3/vol4no3-3.pdf http://s15.postimg.org/drr8j0swb/termite_path.jpg (edited to alter the perspective so that path lines are a little easier to see) Very cool. What software are you using? I can't get my Mathematica graphs to look as clean as that. 
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Very cool. What software are you using? I can't get my Mathematica graphs to look as clean as that. Quoted:
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Invalid starting point. If I remember correctly, 342 sub v means it should have least one valid Hamiltonian circuit from any given point on the outer face. It's obviously an NP-complete problem and I'm not even going to try it on my laptop. Eta: yup http://akcejournal.org/contents/vol4no3/vol4no3-3.pdf http://s15.postimg.org/drr8j0swb/termite_path.jpg (edited to alter the perspective so that path lines are a little easier to see) Very cool. What software are you using? I can't get my Mathematica graphs to look as clean as that. lightwave -> tga for multiple solid object and wireframe layers -> photoshop -> adjust contrast etc -> flatten |
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You're looking for a spatial reasoning problem with a practical application?  Quoted:
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It's more of a logic and spatial reasoning problem than a math problem, and a more or less pointless one at that. (and the answer is obviously yes) You're looking for a spatial reasoning problem with a practical application? There are plenty of spatial reasoning problems that have practical applications. I use them as examples in my classes all the time (I teach machine design, and have been a professional machine designer for a number of years). Problems like those often encountered in GD, however, generally amount to calculating the topography of one's navel, to use Douglas Adams' terminology. That is, if they're not ridiculous questions in the first place. |
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There are plenty of spatial reasoning problems that have practical applications. I use them as examples in my classes all the time (I teach machine design, and have been a professional machine designer for a number of years). Problems like those often encountered in GD, however, generally amount to calculating the topography of one's navel, to use Douglas Adams' terminology. That is, if they're not ridiculous questions in the first place. Quoted:
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It's more of a logic and spatial reasoning problem than a math problem, and a more or less pointless one at that. (and the answer is obviously yes) You're looking for a spatial reasoning problem with a practical application? There are plenty of spatial reasoning problems that have practical applications. I use them as examples in my classes all the time (I teach machine design, and have been a professional machine designer for a number of years). Problems like those often encountered in GD, however, generally amount to calculating the topography of one's navel, to use Douglas Adams' terminology. That is, if they're not ridiculous questions in the first place. I think this issue is one of semantics and is therefor rather subjective, but I'm sure "practical application" means something entirely different to someone interested in machine design then it does a Mathematician. It's like a engineer arguing the irrelevance of a theorem designed for "n-dimensions" when he just needs 3. The beauty of this problem was not in its difficulty to solve, or the train of thought it provoked, but rather its difficulty to prove mathematically. So far, no one has. |
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Wouldn't his last layer have to be done in a closing spiral to end up at the center? ETA: I vaguely remember something called a Hamiltonian (in 3d vector calc, maybe?) but that was many many beers ago. Quoted:
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Easy. http://imgur.com/SJsrSPZ http://imgur.com/SJsrSPZ (Starts at the center of the outside face, moves through all the squares to the upper right corner, enters the next slice at the upper right corner and moves through all the squares to the lower leg corner, enters the center slice ay the lower left corner and moves through all the squares except the center one, enters the 4th slice at the square 1 right of center amd moves through all of the squares except the center one, enters the back face in the lower left corner and moves through all the squares, ending on the center square of the back face. Then proceed back to the center of the 4th slice, and finally back to the center of the middle slice to complete) If you're looking for a mathematical proof of this, then sorry. (Not sure if I did something wrong with the picture) That's correct.
At least, that's one of the ways to do it. Wouldn't his last layer have to be done in a closing spiral to end up at the center? ETA: I vaguely remember something called a Hamiltonian (in 3d vector calc, maybe?) but that was many many beers ago. What do you mean by that? It ends up at the center of the last "slice", but it doesn't have to be in a spiral. A 5x5 grid you can start at any point and finish at any other point on the grid. |
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I think this issue is one of semantics and is therefor rather subjective, but I'm sure "practical application" means something entirely different to someone interested in machine design then it does a Mathematician. It's like a engineer arguing the irrelevance of a theorem designed for "n-dimensions" when he just needs 3. The beauty of this problem was not in its difficulty to solve, or the train of thought it provoked, but rather its difficulty to prove mathematically. So far, no one has. Quoted:
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It's more of a logic and spatial reasoning problem than a math problem, and a more or less pointless one at that. (and the answer is obviously yes) You're looking for a spatial reasoning problem with a practical application? There are plenty of spatial reasoning problems that have practical applications. I use them as examples in my classes all the time (I teach machine design, and have been a professional machine designer for a number of years). Problems like those often encountered in GD, however, generally amount to calculating the topography of one's navel, to use Douglas Adams' terminology. That is, if they're not ridiculous questions in the first place. I think this issue is one of semantics and is therefor rather subjective, but I'm sure "practical application" means something entirely different to someone interested in machine design then it does a Mathematician. It's like a engineer arguing the irrelevance of a theorem designed for "n-dimensions" when he just needs 3. The beauty of this problem was not in its difficulty to solve, or the train of thought it provoked, but rather its difficulty to prove mathematically. So far, no one has. Ain't that the truth. Four, actually, but sometimes more. |
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Ain't that the truth. Four, actually, but sometimes more. Quoted:
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It's more of a logic and spatial reasoning problem than a math problem, and a more or less pointless one at that. (and the answer is obviously yes) You're looking for a spatial reasoning problem with a practical application? There are plenty of spatial reasoning problems that have practical applications. I use them as examples in my classes all the time (I teach machine design, and have been a professional machine designer for a number of years). Problems like those often encountered in GD, however, generally amount to calculating the topography of one's navel, to use Douglas Adams' terminology. That is, if they're not ridiculous questions in the first place. I think this issue is one of semantics and is therefor rather subjective, but I'm sure "practical application" means something entirely different to someone interested in machine design then it does a Mathematician. It's like a engineer arguing the irrelevance of a theorem designed for "n-dimensions" when he just needs 3. The beauty of this problem was not in its difficulty to solve, or the train of thought it provoked, but rather its difficulty to prove mathematically. So far, no one has. Ain't that the truth. Four, actually, but sometimes more. Time doesn't count. 
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