Three utilities problem has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it. | ||||||||||
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A
fact from this article appeared on Wikipedia's
Main Page in the "
Did you know?" column on
December 20, 2021. The text of the entry was: Did you know ... that it is impossible to
draw non-crossing lines from three houses to three utilities (pictured) in a plane? |
This
level-5 vital article is rated GA-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
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— Preceding unsigned comment added by 50.80.170.239 ( talk) 17:57, 25 February 2015 (UTC)
As the problem is formulated ("Is there a way to do so without any of the lines crossing each other?") the problem should be solvable with the solution "no".
In order to say that the problem has no solution you should formulate the problem as something like "Find a way to do so without any of the lines crossing each other".
I think the best thing is to just say that the answer is no, there is no such way and keep the original problem formulation.
Just my two cents. -- 130.238.5.7 08:49, 22 April 2006 (UTC)
In the article referenced by Uncle G the 1979 Mathematics Magazine article that explains the long history of the utilities setting[1] the utilities puzzle only has 1 rule, that the lines cannot cross. Why has there been a rule added that states the lines cannot pass through another company or house? By adding that rule it makes the puzzle unsolvable in 2D but I don't know why that rule would be added. The puzzle can be found on the internet without that rule so it should at least be mentioned that some variations don't have that rule.
In the magazine article there are 2 older versions. 1 of the older versions is about 3 families who hate each other but wish to go to the market, the church and a third place. This version does not imply that the path to the church could not pass through the path to the market thus making the puzzle solvable.
The version with paths to wells implies that you can't cross over the stations because they are wells but 2 of the 3 do not.-- 220.136.176.147 ( talk) 16:12, 16 June 2011 (UTC)
According to the external link at Archimedes lab.org the rules do not say that you cannot run a line through a house. Thus the rules are wrong here on Wikipedia. 'Alternative solution 1 Nevertheless, this puzzle is possible to solve by using subterfuge... The only way this can be done without the lines crossing is by allowing one of the lines (it doesn't matter which one) to enter a house or a utility company and then emerge from the building on the other side. In fact, the wording of the puzzle is a bit imprecise and doesn't forbid lines to go through the houses or to use the third dimension!'
According to the rules at cut the knot the rules do not say you can't run a line through a house. 'The puzzle is to lay on water, gas, and electricity, from W, G and E, to each of the three houses, A, B and C, without any pipe crossing another.'
The 3D graph solution is being pushed above all other solutions and thus the rules are being altered. This ruins the usefulness of the puzzle which for me is a simple practice experiment in divergent thinking. With the rules stated properly the easiest solution is a line passing through a house.
I agree with the above. The historical "water, gas and electricity" puzzle has the intended solution of going through a house. The article would be better with the simpler formulation, and a diagram of the intended solution, as well as a proof that there is no solution with the houses and utilities as points (or a reference to such a proof, since I guess it's already somewhere on the topological part of wikipedia). JoDu987 ( talk) 16:24, 15 April 2012 (UTC)
I've worked for a pipeline company before. You HAVE to use common sense in this case.
For one: These are NOT 'dots'. These are houses, actual 'area' in squared feet. And two: NO company in their right mind would provide direct lines of service to houses, they try to avoid that since it costs money. Instead they have one 'main-line' that branches off to houses.
And since the houses/cottages occupy 'area' and are NOT 'non-existant/non-area points', the houses can accept branched pipes.
http://en.wikipedia.org/wiki/Image:3-cottage_solved.JPG —The preceding unsigned comment was added by Mix Bouda-Lycaon ( talk • contribs) 10:18, 25 January 2007 (UTC).
The reply "I've worked for a pipeline company before. You HAVE to use common sense in this case" is silly and irrelevant, because the true common-sense answer is that this problem just doesn't come up; there's always a practical solution of some kind, usually a simple one. This is a concept in mathematics/geometry/whatever, made easier to visualize by imaginary houses and imaginary utility lines, and the added rules only prevent people from missing the point. It's not an engineering problem and engineering solutions don't count, because the problem is so ridiculously easy even for a novice engineer (using real houses and real utilities) that it's not even worth mentioning. TooManyFingers ( talk) 15:42, 30 June 2021 (UTC)
There's a game based on this idea, played in many a school exercise book. And there's a solution (sort of), if drawn on paper where a line would cross punch a hole draw the line past it on the other side and punch a hole back through to join it to the last house! (no don't take it seriously!-- Kingrandomfan ( talk) 18:06, 8 June 2010 (UTC))
The result of the move request was: Not moved. ( non-admin closure) – Ammarpad ( talk) 17:17, 1 November 2018 (UTC)
Three utilities problem →
Utility graph – The current title is a misnomer — this is not a “problem” in any of the senses used in mathematics, at best it could be called a "puzzle" or a "riddle". Most of the article is of interest to graph theorists, therefore i recomment making the graph the primary subject of the article.
Nowak Kowalski (
talk) 16:15, 25 October 2018 (UTC)
The "proof without words" section really did help me to understand the situation faster and more clearly. I truly think it's very well done. But I find it a bit comical that the part of it that helped me the most was the paragraph-length caption full of ... words. :) TooManyFingers ( talk) 15:24, 30 June 2021 (UTC)
This puzzle is not impossible to solve. One simply routes one of the utilities through the middle house so that "all houses are supplied with all utilities without the lines crossing". There is nothing in the instructions to say that you can't go through a property to reach another, is there? Mjroots ( talk) 17:30, 20 December 2021 (UTC)
The link on WP's main menu today states, "...it is impossible to draw non-crossing lines from three houses to three utilities (pictured) in a plane?" My initial reaction is to wonder if that is also true if you are in a car or just walking? :-) Just my 2-cents! Thomas R. Fasulo ( talk) 20:52, 20 December 2021 (UTC)
the mobius strip doesnt work because the blue and yellow line still have to cross ... the only solution is to add another dimension .. allowing one to go through the middle or leave the plane the items are on ... 2607:FEA8:BD1F:5910:804B:D7C7:6F9C:12FE ( talk) 21:54, 17 February 2023 (UTC)
Three utilities problem has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it. | ||||||||||
| ||||||||||
A
fact from this article appeared on Wikipedia's
Main Page in the "
Did you know?" column on
December 20, 2021. The text of the entry was: Did you know ... that it is impossible to
draw non-crossing lines from three houses to three utilities (pictured) in a plane? |
This
level-5 vital article is rated GA-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
— Preceding unsigned comment added by 50.80.170.239 ( talk) 17:57, 25 February 2015 (UTC)
As the problem is formulated ("Is there a way to do so without any of the lines crossing each other?") the problem should be solvable with the solution "no".
In order to say that the problem has no solution you should formulate the problem as something like "Find a way to do so without any of the lines crossing each other".
I think the best thing is to just say that the answer is no, there is no such way and keep the original problem formulation.
Just my two cents. -- 130.238.5.7 08:49, 22 April 2006 (UTC)
In the article referenced by Uncle G the 1979 Mathematics Magazine article that explains the long history of the utilities setting[1] the utilities puzzle only has 1 rule, that the lines cannot cross. Why has there been a rule added that states the lines cannot pass through another company or house? By adding that rule it makes the puzzle unsolvable in 2D but I don't know why that rule would be added. The puzzle can be found on the internet without that rule so it should at least be mentioned that some variations don't have that rule.
In the magazine article there are 2 older versions. 1 of the older versions is about 3 families who hate each other but wish to go to the market, the church and a third place. This version does not imply that the path to the church could not pass through the path to the market thus making the puzzle solvable.
The version with paths to wells implies that you can't cross over the stations because they are wells but 2 of the 3 do not.-- 220.136.176.147 ( talk) 16:12, 16 June 2011 (UTC)
According to the external link at Archimedes lab.org the rules do not say that you cannot run a line through a house. Thus the rules are wrong here on Wikipedia. 'Alternative solution 1 Nevertheless, this puzzle is possible to solve by using subterfuge... The only way this can be done without the lines crossing is by allowing one of the lines (it doesn't matter which one) to enter a house or a utility company and then emerge from the building on the other side. In fact, the wording of the puzzle is a bit imprecise and doesn't forbid lines to go through the houses or to use the third dimension!'
According to the rules at cut the knot the rules do not say you can't run a line through a house. 'The puzzle is to lay on water, gas, and electricity, from W, G and E, to each of the three houses, A, B and C, without any pipe crossing another.'
The 3D graph solution is being pushed above all other solutions and thus the rules are being altered. This ruins the usefulness of the puzzle which for me is a simple practice experiment in divergent thinking. With the rules stated properly the easiest solution is a line passing through a house.
I agree with the above. The historical "water, gas and electricity" puzzle has the intended solution of going through a house. The article would be better with the simpler formulation, and a diagram of the intended solution, as well as a proof that there is no solution with the houses and utilities as points (or a reference to such a proof, since I guess it's already somewhere on the topological part of wikipedia). JoDu987 ( talk) 16:24, 15 April 2012 (UTC)
I've worked for a pipeline company before. You HAVE to use common sense in this case.
For one: These are NOT 'dots'. These are houses, actual 'area' in squared feet. And two: NO company in their right mind would provide direct lines of service to houses, they try to avoid that since it costs money. Instead they have one 'main-line' that branches off to houses.
And since the houses/cottages occupy 'area' and are NOT 'non-existant/non-area points', the houses can accept branched pipes.
http://en.wikipedia.org/wiki/Image:3-cottage_solved.JPG —The preceding unsigned comment was added by Mix Bouda-Lycaon ( talk • contribs) 10:18, 25 January 2007 (UTC).
The reply "I've worked for a pipeline company before. You HAVE to use common sense in this case" is silly and irrelevant, because the true common-sense answer is that this problem just doesn't come up; there's always a practical solution of some kind, usually a simple one. This is a concept in mathematics/geometry/whatever, made easier to visualize by imaginary houses and imaginary utility lines, and the added rules only prevent people from missing the point. It's not an engineering problem and engineering solutions don't count, because the problem is so ridiculously easy even for a novice engineer (using real houses and real utilities) that it's not even worth mentioning. TooManyFingers ( talk) 15:42, 30 June 2021 (UTC)
There's a game based on this idea, played in many a school exercise book. And there's a solution (sort of), if drawn on paper where a line would cross punch a hole draw the line past it on the other side and punch a hole back through to join it to the last house! (no don't take it seriously!-- Kingrandomfan ( talk) 18:06, 8 June 2010 (UTC))
The result of the move request was: Not moved. ( non-admin closure) – Ammarpad ( talk) 17:17, 1 November 2018 (UTC)
Three utilities problem →
Utility graph – The current title is a misnomer — this is not a “problem” in any of the senses used in mathematics, at best it could be called a "puzzle" or a "riddle". Most of the article is of interest to graph theorists, therefore i recomment making the graph the primary subject of the article.
Nowak Kowalski (
talk) 16:15, 25 October 2018 (UTC)
The "proof without words" section really did help me to understand the situation faster and more clearly. I truly think it's very well done. But I find it a bit comical that the part of it that helped me the most was the paragraph-length caption full of ... words. :) TooManyFingers ( talk) 15:24, 30 June 2021 (UTC)
This puzzle is not impossible to solve. One simply routes one of the utilities through the middle house so that "all houses are supplied with all utilities without the lines crossing". There is nothing in the instructions to say that you can't go through a property to reach another, is there? Mjroots ( talk) 17:30, 20 December 2021 (UTC)
The link on WP's main menu today states, "...it is impossible to draw non-crossing lines from three houses to three utilities (pictured) in a plane?" My initial reaction is to wonder if that is also true if you are in a car or just walking? :-) Just my 2-cents! Thomas R. Fasulo ( talk) 20:52, 20 December 2021 (UTC)
the mobius strip doesnt work because the blue and yellow line still have to cross ... the only solution is to add another dimension .. allowing one to go through the middle or leave the plane the items are on ... 2607:FEA8:BD1F:5910:804B:D7C7:6F9C:12FE ( talk) 21:54, 17 February 2023 (UTC)