patrick.net

Onvacation says

The rules say you can't cross any lines, houses and utilities included.

Is there a line crossed?

komputodo says

Is there a line crossed?

All the time.

But seriously, you can't go through houses or utilities. They are made up of lines.

Onvacation says

komputodo says

The rules say you can't cross any lines, houses and utilities included.

It does say on the page that the wording is imprecise and that you can through (the back) of houses.

I would give each house their own resource (like directly on top of it) then they'd all just mete out the rest as needed. Less external piping needed. Until corruption takes over or lines cross, whatever arbitrary rules there are.

mell says

It does say on the page that the wording is imprecise and that you can through (the back) of houses.

Nope.

DhammaStep says

I would give each house their own resource (like directly on top of it) then they'd all just mete out the rest as needed. Less external piping needed. Until corruption takes over or lines cross, whatever arbitrary rules there are.

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.

Onvacation says

mell says

It does say on the page that the wording is imprecise and that you can through (the back) of houses.

Nope.

DhammaStep says

I would give each house their own resource (like directly on top of it) then they'd all just mete out the rest as needed. Less external piping needed. Until corruption takes over or lines cross, whatever arbitrary rules there are.

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.

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!

mell says

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.

Nope. There is a solution that doesn't cross any lines. It does require that you use both sides of the paper.
mell says

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!

Our math teacher did lay out the rules a little more precisely than I first did.

Onvacation says

Nope. There is a solution that doesn't cross any lines. It does require that you use both sides of the paper.

Does it require folding it like they say, i.e. taking advantage of 3 dimensions? And is it the solution on their Facebook page? Just so if I find some time that I don't look it up beforehand

https://en.wikipedia.org/wiki/Three_utilities_problem

mell says

Does it require folding it like they say, i.e. taking advantage of 3 dimensions? And is it the solution on their Facebook page? Just so if I find some time that I don't look it up beforehand

Kind of.

Hint: You need to use both sides of the paper, with a twist.

According to Wiki' this is a math problem. But what do they know.

I have always been fascinated how technology sometimes follows theoretical math. For instance, the concept of imaginary numbers grew from some mathematicians trying to get over the enigma of the square root of a negative number.
https://www.jioforme.com/imaginary-numbers-may-be-essential-to-explain-reality/233257/

Onvacation says

Try it. You will find that one of the lines is still blocked.

Ah, why did it make sense earlier?

Onvacation says

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.

Your teacher is an idiot, komputodo's solution is not only brilliant it is correct. The exercise is you can't intersect lines. Water runs under foundations. So of course you can run it under the houses. Also for this to be a problem it has to have a solution. If not it's just a parlor trick, a paradox. Was it meant to be solved, then it is a more valid solution than some of those on that link that was posted. Where the page was made into a cylinder with a strap extension. The rules didn't say anything about that either.

It's not quite on a flatland, but on a spherical surface: borderless but finite surface. Once visualize that way, the solution is quite straight forward.

OTOH, a more common situation in the real world was in designing two-layer or multi-layer printed circuit board, so punching holes connecting to a different layer was the common solution of achieving the "edge wrap-around."

Onvacation says

Hint: You need to use both sides of the paper, with a twist.

Tenpoundbass says

Also for this to be a problem it has to have a solution.

Not all problems have solutions, but this one does.

And it's not Komputodos

qroproton says

Onvacation says

Hint: You need to use both sides of the paper, with a twist.

Nope. Those lines would have to cross on the backside.

Onvacation says

Nope. Those lines would have to cross on the backside.

Hell! You are right.

Onvacation says

Hint: You need to use both sides of the paper, with a twist.

Now you're taking the stance that there is only one solution, while ignoring the solutions provided. When Komputodos is the actual most practical, and how signals, lines, and connections are routed in the real world. Nothing in the real world goes to the other side of the world and comes up the other side. 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.

Are you allowed to put holes in the paper too, so the route can go to the back of the paper via the hole, so the intersecting line can continue on the other side of the hole where the line didn't intersect?

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.

When do we get to see the solution?

qroproton says

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.

Doesn't work, electric and water lines cross on the back of the paper.

This has no solution I don't think. I spent about an hour simplifying it in my head last night.

It seems like being able to go over to the other side of the paper would be an advantage, but them I realized that's the same constrains you have on a sphere. A sphere is really no different than a flat surface - take a sphere, poke one hole in it, then stretch that hole out to a square. All a flat sheet is is a sphere, missing a single point.

Doesn't matter where you place the homes and utilities either.

You cannot solve this if you are restricted to 2 dimensions. Hence the name "Flatland".

It's an interesting conundrum, and I think it's best aspect is that it points out that many problems cannot be solved if you limit yourself to restrictions put upon you by others (including nature) and that thinking outside of the box is what allows the impossible to become possible.

As an example, while faster-than-light travel may not be physically possible as we know it, the same effect, that is, to travel great distances in reasonable time, might be achievable through other means. eg. Wormholes.

Onvacation says

Hint: You need to use both sides of the paper, with a twist.

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.


Tenpoundbass says

Are you allowed to put holes in the paper too, so the route can go to the back of the paper via the hole

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!

Tenpoundbass says

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.

I disagree. It's problems like this that make youngsters think. Even though the current culture discourages critical thinking over "Googling" we need critical thinkers to solve todays. and tomorrows, problems.

The problem introduces graph theory for which this particular problem has no planar solution. The answer, at least the one I discovered, was inspired by topology.

It is certainly possible to have a great life with no formal education but in good schools with good professors we learn of problems and solutions that scientists and mathematicians have worked on over the eons. Like Newton said, "I stand on the shoulders of giants."

This is not a practical problem. It's a "thought exercise". It has constraints. There are probably more than one solutions but the solutions offered so far in this thread have violated the constraints.

Tenpoundbass says

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.

Now that is "thinking outside of the box". Us ninth graders tried that one as well. Mr. Schultz, our math teacher, said, "Nope."

richwicks says

This has no solution I don't think.

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!

Thanks for playing all of you that did.

Onvacation says

Now that is "thinking outside of the box". Us ninth graders tried that one as well. Mr. Schultz, our math teacher, said, "Nope."

Sounds like he was just favorizing his solution.

Onvacation says

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.

Take this problem for instance, there is no practical application for this, then it's just a factoid nothing more than a trivial notation.

https://www.youtube.com/watch?v=094y1Z2wpJg

Tenpoundbass says

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.

The torus was one of the suggested solutions on the page you linked earlier as well though, iirc.

I don't think you can easily, if at all, create a torus from a single piece of paper. I guess you could, but that is not the moebius solution I came up with.

Funny story.

I looked up Mr. Schultz when I discovered the solution to this problem. At first he was skeptical, but agreed that I had found the solution after I explained it to him.

I asked him if he was still teaching. He replied that he was now a construction manager as he got tired of dealing with the educational bureaucracy and low pay.

Onvacation says

Only solutions that obey the constraints are correct. one piece of paper, front and back, no utility lines cross, all houses get all utilities.

Going through the houses did not violate that principle and having a hole punched on the page didn't violate that principle.

Punching a hole in the page is the toroidal solution IMO, as you can't take a sheet of paper and create a toroid without cutting away everything that is not the toroid.
But in reality all you need is a 2D donut shape. With the center cut out. Then at that point having the edges rounded or left square is semantics.
So if you're allowed to trim away paper for a toroidal shape, but not just punching a hole in a flat paper to achieve the same outcome. Then it's just favoritism of the accepted answer.

I find in Computer programming there are more than one way to achieve the same outcome. None of them are the right way, or the wrong way. But only by how they are used in context to the over all project.

Tenpoundbass says

you can't take a sheet of paper and create a toroid without cutting away everything that is not the toroid.

Roll it up into a tube and staple the ends together.

Can this problem be solved on a donut? I never tried it.

Tenpoundbass says

I find in Computer programming there are more than one way to achieve the same outcome.

And once you find a workable solution you often stop finding a better solution, no matter how crude and inefficient your solution is.

Automan Empire says

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!

Yeah I have a Randall ProTube 1000 II that has and ugly single sided board, and is jumpered with ribbon cables and molex connectors.
I want to point to point the amp. My Amp tech buddy put it on his bench, he is an authorized HiWatt manufacturer. He gave it back and said it looked like it was made with a bunch of surplus components that they had. So they designed the circuit around what they had on hand, and not the other way around.
I love the sound of it, but Caps from the 80's and some of the other components aren't as spry as they were when they were built in the late 80's.
I think he is just a gear snob and didn't want to be bothered with having to redesign the circuit to achieve the desired voltage on the plate and output, I would have been looking for. Or thought I couldn't afford him doing so.
It's not like I'm looking for a Fender Baseman clone circuit, or I would just buy the kit.

Onvacation says

And once you find a workable solution you often stop finding a better solution, no matter how crude and inefficient your solution is.

That is how you become a dinosaur. I have several solutions for almost every problem, as the solution evolves as the use case reveals itself. A simple quick and dirty solution, just allows you to concentrate on more important areas of concern. Then as the project evolves, more elegant solutions evolve. Then those become obsolete, as the complex object, pass through and to objects and routines, may reveal speed or resource issues. I'm always refining methods and ways I do things. I value my collection of bad ideas more than my collection of great ideas. As my bad ideas collection is an invaluable tool when you get enough experience behind it. My Code end up always deploying bug free, while collogues and other teams I warned about the pitfalls of the routes they were taking. Only to get to give them a Trump smile when someone else tells them, "He told you so!".

I owe all of my coding efficiency to my collection of very bad ideas. If you know all of the stupid shit you shouldn't do, then you're only left with all of the sensible options.