The Gas, Water and Electricity Problem
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- Опубліковано 17 лис 2024
- This problem is perhaps the perfect introduction to graph theory: How do you connect Mr Angry, Mr Beastly and Mr Cross to gas, water and electricity without the connections crossing one another?
Robin Wilson, Gresham Professor of Geometry, explains the problem and shows how the suitable diagram can prove that a solution is impossible.
This is the 20th part of 'A Millennium of Mathematical Puzzles'.
The full lecture is available (in 24 parts) here on UA-cam, or it can be downloaded (like all of our lectures) in its complete form from the Gresham College website, in video, audio or text formats:
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Finally. Thank you professor, I've had this bouncing around in my brain for about 30 years. Silly, someone presented it to me saying there was a solution. Good to finally have my theory confirmed.
Angelo Reyes a video of you solving it or you're full of it.
+P. De Rop It can only be done on a "donut", but not a flat plane.
CommanderCorner Which translates to : you can't do this puzzle unless you change the rules .. gotcha :)
+P. De Rop The challenge never specifies that it must be solved on a 2 dimensional surface. The entire point of a puzzle like this is to think outside the box to find a solution. The fact that you're so willing to trap yourself into unnecessary parameters says a lot about you.
+CommanderCorner nope - the puzzle has to be done on a sheet of paper. You want to make a different puzzle - fine - no problem with that.
omg I can't believe I found this on the internet,it's been bugging me since before my son was born-he's just had his 26th birthday!!I thought maybe I'd dreamt it as no one else remembered it lol there was a huge money reward when this first came out-if anyone remembers this then please tell me I'm sane lol
at last an video that is actually worth watching because it show's the facts and not just dumb ways to cheat around a problem x)
the're still a missing line on this solution...and still a missing line on mine...ill begin to think that this problem has no solution
I was wondering: can you design a puzzle with the same rules, being impossible to solve in 3 dimensions? It can be 100 houses, 1000 suppliers, 5 groups that have to interconnect, whatever. Is it possible to make such problem impossible?
My intuition tells me in theory you can't, even if it's ridiculously complex you can always 'interconnect' any set of groups in 3 dimensions. But it's hard to proof and if it's true, it doesn't make sense you can do it easily in 2 dimension.
I just used this for an answer in a graph theory exam this evening. Actually, a K3,3 or K5 graph is a subdivision of a graph G if and only if G is not planar.
It's teoretic possible.
For the last connection, you just drilling a hole throught the earth and comming out on the other side on the earth with the line.
Then you can make it to the last building, if you don't consider two lines passing on each side of the earth are crossing each other.
When I hear about this problem it was forbidden to cross the lines OR go throught another building.
Funny how so many people claim they have solved it, yet none present the answer. I wonder if any of them aren't really lying and believe what they are saying.
you run water electric and gas through each of the utility companies and through each house
W----E----G=====1===2===3
run the lines parallel to each other
gnovakIII
That would be considered splicing i believe
Angelo Reyes
You don't.
you draw it on a bagel...
there are three houses and a gas, water, and electricity station. connect each house to the three of them without crossing any lines. arrange the houses as you wish, i think it is impossible.
So, explain please how are you able to solve it on a piece of paper i.e. 2D without crossing lines (and without cheating e.g using windows and doors). ;-)
The problem is impossible if not solved on a 3D object. That’s the point of the puzzle, to get you visualising mathematics in physical applications.
At least that’s where I’ve heard it most used.
why cant the lines cross the edges of the hexagon?
i don't still get it
It actually is possible, but not on a flat plane.
Correct. In fact, it cannot be done on any 2D plane, even if it is not flat.
+Julien Giovinazzo It's possible - if you allow infinite pipes.
Julien Giovinazzo really, it is possible I have found the trick 😂 it's soo easy.
ua-cam.com/video/JdToKCBSCnU/v-deo.html
class pull out your bagels...
try watching the whole video next time
In 2d this cannot be done. However when you move to 3d it can. I saw a solution that uses a bagel! The final line goes through the center.
The bagel idea is still 2D, because its drawn on its surface. Just another 2D Manifold :D
connect water to a,b,c with direct lines down almost forming a "unfinished triangle". then connect gas to c overhead, gas to b then gas to a, electric to c half moon on right, electric to b half moon and electric to a half moon .
Solution: Draw a verticle line through the top middle wall instead of a horizontal rout.
Yep, i checked it like 4 dozen times. It was twisty and turney and it was a tight squeeze here and there but damn it i got it!
haha I just did a diagram similar (but wasn't a hexagon), anyway hearing it from a professional makes me feel less of a dumb for not being capable.
@Venergon "assumed" means IT IS NOT SPECIFIED, nor disallowed. So, it is part of the solution.
put some pipes under the other houses
I still think about this shit my science teacher asked us to solve in 6th grade..and I'm 42..
It's a puzzle, but someday, a solution to this problem can be done,
i solved it! just put the cables on top of each other, dont go through them.
@surield In the video, the lecturer states that this is the 9th connection and is impossible.
wait a minute, the B is not connected to water! water only has 2 lines going out!
Easy. I solved it in under three minutes.
i can't hear the question. Can someone reply what it is? I love challenges ^ ^
thanks : D sorry for bugging you. I don't have speakers or headphones : )
Connect the electrical station to the water source. Then connect the water source and gas source to the 3 houses. There u go, all houses get electricity, water and gas. Water is a good conductor of electricity after all : D
Ty professor, you show em!
fold the paper so water touches the middle house haha
Herp - No restrictions on 2D or 3D
Electricity through power polls
Gas on ground
Water underground through pipes.
Puzzle Logic'd
Think outside the box !
The edge of the paper is not a boundary, the real world is round.
The is literally a way around it.
That's the one my dad used on me when I was little... I think the answer is also yes if you move 2D across a 3D object (like a cup)
you can do this if you lived on a torus though
Obviously if you take into consideration a 3rd dimension the lines don't need to connect at all, however since the original puzzle is in 2D it's just a great way to piss people off by trying to solve it :P
a piece of paper is a finite plane and if these planes have two sides to them you can go round the other side of the plane without crossing lines to make the 9th connection . surely this sort of plane is actually quite a good fit for the earth , and you could do it , but it would be prohibitively expensive .
I no how erase water to house A and change it to house B then write house A try tht
Did you do it in 2D and everything?
@Nlaw18 in order to keep the universe flat and not cross any lines at all just plain and simply tape the edges of 2 sides of the paper so that it makes a cylinder type shape and and draw some of the lines going around the paper like a globe, this answer is correct because i am not breaking any rules or laws of physics keeping the universe flat from having any other dimension added like depth and i kept the universe to just 2 dimensions and therefore correct i could go into further detail but...
@SeeYaOnSondee it is possible on 2D as well, with dimensionnles common points on the border corespondence points in another 2D plan so it's possible in 2D with 2 Differrent spaces:D
@Nlaw18 i have no idea if my last response went to you cuz im having internet issues. but anyways i just explained why some of the cheats do not work such as going through a house because they neighbor would just cut the line or folding a corner of the paper,because in a 2d universe folding the paper would cause it to stil be flat and therefore still cross and popin a hole and drawing on the otherside wont work because there is no height in a 2d world and therefore impossible but the answer is
Actually Electricity can be transformed through air (which avoids psychical crossing) through electric poles (transformator inside doesnt have actual line of electricity and transported throught electic field),
I figured out a way to solve this puzzle without using a donut shape. Just a simple piece of graph paper. This thing can be solved. I'll make a video eventually.
There is a 2d way to do this without special shapes- think of the placements.
Lol epic fail joke at the end there was just silence and tumbleweed
Real world soloution is for B, and C to share C's connection to water. Or if this was a circut board, you would simply burn a trace on the backside of the board from B to Water.
Chuck Norris ate a paper with the problem and he shitted it with the answer!
go through the gaps in the lines
The answer is simple mr.beastly is amish and doesn't need electricity.
I tried it myself and i got it correctly 100% not touching other utilities and none left behind
how
HOUSE B DOESN'T HAVE ANY WATER!!
It is possible. It's actually VERY easy.
as he said at the end of the video, you have to cross through a house or utilities thingy to complete the puzzle or else it is impossible
It is impossible to solve as it is. But in 3D it is possible.
If the riddle is asked to be solved in a scenario that is live like, on a round object (earth)
and the lines cannot cross, and you cannot dig or lift the lines. then the riddle is IMPOSSIBLE to solve.
BUT, if the riddle is asked to be solved on a piece of paper.. then it is solvable, but still VERY hard to solve.
in this puzzle you just draw through the spaces in the lines
House B has a well system. Solved.
So the solution is, why not all the neighbours reside in a 3 storied apartment where they can access all the utilities... 😂
Link water, heat, and electricity together, then draw heat to A, water to B, and Electricity to C.
What now?
Yes you can....pick up the paper.....witch is not against the rules or go true the house.
its easy, have the line from b go around c, through the electricity, then to the water.
where is the line...C to W ?....9 lines ? or 8
@DimitrisMPapadakis
Being 2-dimensional is assumed in the puzzle.
@HuntingMasterz he must have listened to it with no sound i guess
what if the lines go behind the houses
How?
I've completed it and I am 12
@Alucard20039 how?
It is posseble, you can go on the end fron W to in the middel EB than over e to C
THE SOLUTION IS TO CONNECT GAS, WATER AND ELECTRICITY TO A SUBSTATION( SEPARATE HOUSE) BY ONE LINE FROM EACH STATION. THEN YOU SIMPLY DRAW ONE LINE TO EACH HOUSE FROM THIS SUBSTATION..THIS LINE REPRESENTS GAS,WATER AND ELECTRICITY IN PARALLEL TO EACH OTHER AND THEY WILL NOT CROSS....DRAW IT OUT AND SEE THAT IT WORKS.......
this shit is answered by my philo1 teacher but i didnt bother to listen or look at it. im playing ragnarok on my lappy. too bad for me :C i didnt realize that this puzzle is famous
put a bridge over the electricity to house b, and no I don't mean a walking bridge I mean an electrical bridge
I did it, i put in a bridge and my water pipe went over that.
you missed one on the water
Connect the gas to the water with a line and the electricity to the water with a line , then from the water plant draw 3 lines one to each house. total five lines not crossing
Can't mix them
cant do this cos if u put electric to water then u will get electrocuted
doesn't say you can't mix just you can't cross
you won't get electrocuted if you have plastic pipes in the house, copper outside which is insulated plus use ultra pure water as it doesn't conduct electricity
When you use water, you don't want them to be in a *current*.
this puzzle IS solvable, you just need to do it on a doughnut shape
you can't draw it in a plane but you may try to draw it on a bus, but you will probably fail on the bus as well :)
I figured it out
water on house B?????
It is solvable if the supply goes through the door and out the window to the next house
Make it 3D. Then a line can go over another one.
Solve!
the B house get the Water through the Gas Company!
It doesn't cross any line.
Should have work, because Gas Company doesn't hate any of them.
SOLVED!!
btw, i m 7yo...
and my father told me to.
Umm, the second house isn't connected to the water...
this could be solved by applying the pocket dimension theory
Electricity travels above ground
This is actually unsolvable
@SeeYaOnSondee the problem is in 2h, 3d dont mean shit here lol
@Vranje4ever well, I don't know much about math, but I DO know that this problem is solvable on a doughnut shape. I invite you to take a look at my video of me solving it, and give any constructive feedback. I also know that this problem IS impossible to do on a flat piece of paper (without using "windows" or "a water tower" as I have seen in other videos...), however, when drawn on a doughnut, which is not a normal shape, since it has a hole in it, it IS indeed possible to accomplish.
A donat is an 3D object, but the surface is as any surface 2D ...
just hook a cable onto the neigbours house and there you go
But not a sphere if i'm not mistaken.
Make underground pipes :D
Problem gauss?
Yes
go between the spaces in the dotted lines XD
i solve this in my second try 15 years ago
Hous B has no water
well i guess im goin with DimitrisMPapadakis on this one there are 2 dimensions but i did it on a 2d plain. make a horizontal line with the houses and a vertical line with the utility's. elec first on top ,gas in middle, and water on the bottom floor and use one line on every utility Horizontal though. just think how its already put together
it is posible, you can do this
you can solve this puzzle if you use quantum uncertainty ...