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Try it. You will find that one of the lines is still blocked.
Nope.
Us 14 year old's thought of these solutions and our teacher rejected them. I probably spent more time on this problem than homework for math or my other classes.
Also for this to be a problem it has to have a solution.
Onvacation saysHint: You need to use both sides of the paper, with a twist.
Hint: You need to use both sides of the paper, with a twist.
If you remove the line from House 2 to Gas, then redraw it going up, around the other side of the page, and then up to Gas, that allows you to run a line from House 3 to the edge of the page, then across the backside emerging on the LHS of the page so that you can connect to Water.
Hint: You need to use both sides of the paper, with a twist.
Are you allowed to put holes in the paper too, so the route can go to the back of the paper via the hole
It's pointless mental exercises like these that have dumbed down two generations. It seems all of the cheat answers are more accepted, than how things are actually done in practice.
Use a hole puncher, and punch a hole above H2m run the H20 line going to the H3, into the hole to come up the other side, as it is now on the right.
Run H1 electric on the front of the page, by routing it to the far left side of the page, and running it up to the left of the hole, and up to H1.
This has no solution I don't think.
You can just tell us, no need to be a Mobius Dick about it. ☜(゚ヮ゚☜) This takes us out of two dimensions however, as does the solution of projecting it onto a torus.
Now that is "thinking outside of the box". Us ninth graders tried that one as well. Mr. Schultz, our math teacher, said, "Nope."
No planar solution.Automan Empire says
You can just tell us, no need to be a Mobius Dick about it. ☜(゚ヮ゚☜) This takes us out of two dimensions however, as does the solution of projecting it onto a torus.
Automan got it!
If you can project it onto another dimension, and that is accepted as a valid solution. Then all solutions are valid. As it's only a thought exercise, with no one true answer.
Only solutions that obey the constraints are correct. one piece of paper, front and back, no utility lines cross, all houses get all utilities.
you can't take a sheet of paper and create a toroid without cutting away everything that is not the toroid.
I find in Computer programming there are more than one way to achieve the same outcome.
Everything but the simplest 555 timer or add-2-caps-and-a-pot amplifier chip circuits use 2 sided circuit boards with plated-through vias or holes. The first single sided circuit boards that replaced discrete components connected point to point in 3 dimensions needed wire jumpers over the component side to solve this problem. Board architecture for compactness sometimes has sub-boards jumpered in perpendicularly or in a parallel plane, often using a flexible PCB and headers for the jumper itself. Then there are boards designed for automated parts placement all in lines; good luck trying to intuit the schematic by looking at one of these!
And once you find a workable solution you often stop finding a better solution, no matter how crude and inefficient your solution is.
If you know all of the stupid shit you shouldn't do, then you're only left with all of the sensible options.
Tenpoundbass saysIf you can project it onto another dimension, and that is accepted as a valid solution. Then all solutions are valid. As it's only a thought exercise, with no one true answer.
Only solutions that obey the constraints are correct. one piece of paper, front and back, no utility lines cross, all houses get all utilities.
I contend there is no solution, but it's a good problem for students. Some problems can't be solved. That's a lesson a lot of people never learn.
richwicks saysI contend there is no solution, but it's a good problem for students. Some problems can't be solved. That's a lesson a lot of people never learn.
No planar solution.
Moebius could do it. One piece of paper with a twist. It turns a two sided plane into a geometric shape with one side and one edge.
I agree that some problems can't be solved. Some problems we have yet to prove unsolvable.
@richwicks Looking forward to meeting up with you in person again one of these days.
@richwicks Looking forward to meeting up with you in person again one of these days.
Onvacation says@richwicks Looking forward to meeting up with you in person again one of these days.
I'd be up for that too.
Patrick saysOnvacation says@richwicks Looking forward to meeting up with you in person again one of these days.
I'd be up for that too.
I think we're long overdue for some sort of PatNet meetup.
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The problem: Connect each house with a line from the gas, water, and electricity companies without crossing any lines. You can put the houses and utility companies anywhere you want. You can use both sides of the paper; when your line gets to the edge just continue over to the other side.
My math teacher said if we solved it he would give us an A for the year. On top of that he said if we solved it in high school he would talk to our math teacher and get us an A.
I spent a lot of time the next 4 years attempting but never solving this problem.
It seemed there was always one connection that could not be completed without violating the rules.
Has anyone seen this? Has anyone else solved it?