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Flatland Problem


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2021 Aug 21, 11:47am   4,180 views  77 comments

by Onvacation   ➕follow (3)   💰tip   ignore  

My ninth grade math teacher gave us this problem


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?

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1   Onvacation   2021 Aug 21, 11:50am  

I remembered this problem when Patrick mentioned how problems were solved in dreams. Years after high school I was a math major at Humboldt state and the solution appeared to me in a dream. When I woke up the problem was solved.
2   Tenpoundbass   2021 Aug 21, 12:05pm  

If I'm understanding you right, you said you can run the lines over the back of the paper as well. Then why not run house two's gas from the back, so house three can get to the water by running a line on the right edge following the other two lines?
Onvacation says
3   GNL   2021 Aug 21, 12:06pm  

Best I can do is get all of them except 1.

4   stereotomy   2021 Aug 21, 12:10pm  

Tenpoundbass says
If I'm understanding you right, you said you can run the lines over the back of the paper as well. Then why not run house two's gas from the back, so house three can get to the water by running a line on the right edge following the other two lines?
Onvacation 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.

Where's my A?
5   Tenpoundbass   2021 Aug 21, 12:27pm  

And it's really like the way Liberals usurp everything in the name of Science.
I cringe when someone calls a logistical problem a math problem. Math is using numbers and formulas to solve problems. And once a proof is discovered it can be used on all similar problems. Logistical solutions are unique to the problem at hand, and math may or may not be required.

BTW, you repeated the same solution I posted to you .Where's my "A" in Logistics and Word Semantics?
6   stereotomy   2021 Aug 21, 12:36pm  

Tenpoundbass says
And it's really like the way Liberals usurp everything in the name of Science.
I cringe when someone calls a logistical problem a math problem. Math is using numbers and formulas to solve problems. And once a proof is discovered it can be used on all similar problems. Logistical solutions are unique to the problem at hand, and math may or may not be required.

BTW, you repeated the same solution I posted to you .Where's my "A" in Logistics and Word Semantics?


You get the A, I get an F for poor reading comprehension.
8   Onvacation   2021 Aug 21, 12:40pm  

Tenpoundbass says
If I'm understanding you right, you said you can run the lines over the back of the paper as well. Then why not run house two's gas from the back, so house three can get to the water by running a line on the right edge following the other two lines?

Try it. You will find that one of the lines is still blocked.
9   mell   2021 Aug 21, 12:48pm  

komputodo says


I thought about this solution as well but I'm not sure you're allowed to thread the gray line through the houses.
10   Onvacation   2021 Aug 21, 12:56pm  

stereotomy 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.

Where's my A?

Nope. Try it. You will find that one of the lines is still blocked.
12   Onvacation   2021 Aug 21, 12:57pm  

HunterTits says


Why don't you move the utilities and houses around?

You can do that.
HunterTits says

Also: https://www.archimedes-lab.org/How_to_Solve/Water_gas.html

You will get the solution from that, kind of, but there is a simpler solution.
13   Onvacation   2021 Aug 21, 12:58pm  

Tenpoundbass says
I cringe when someone calls a logistical problem a math problem

I never called it a math problem.
BTW, you repeated the same solution I posted to you .Where's my "A" in Logistics and Word Semantics?

I have not posted a solution.
14   Onvacation   2021 Aug 21, 1:00pm  

komputodo says

Nope. Each house must have a line to each utility.
15   Onvacation   2021 Aug 21, 1:02pm  

komputodo says

The rules say you can't cross any lines, houses and utilities included.
16   Onvacation   2021 Aug 21, 1:06pm  

HunterTits says

Also: https://www.archimedes-lab.org/How_to_Solve/Water_gas.html

We did not have the Internet in 9th grade.

This problem was about the problem solving process. I wasted a lot of paper before I gave up. Then, in college, I studied topology and my brain put it together in my sleep.
17   komputodo   2021 Aug 21, 1:41pm  

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

Is there a line crossed?
18   Onvacation   2021 Aug 21, 1:44pm  

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.
19   mell   2021 Aug 21, 2:12pm  

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.
20   DhammaStep   2021 Aug 21, 2:17pm  

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.
21   Onvacation   2021 Aug 21, 2:22pm  

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.
22   mell   2021 Aug 21, 2:26pm  

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!
23   Onvacation   2021 Aug 21, 2:30pm  

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.
24   mell   2021 Aug 21, 2:38pm  

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
26   Onvacation   2021 Aug 21, 3:04pm  

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.
27   Onvacation   2021 Aug 21, 3:15pm  

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/
28   Tenpoundbass   2021 Aug 21, 6:42pm  

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


Ah, why did it make sense earlier?
29   Tenpoundbass   2021 Aug 21, 6:53pm  

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.
30   Reality   2021 Aug 21, 7:05pm  

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."
31   qroproton   2021 Aug 21, 8:36pm  

Onvacation says
Hint: You need to use both sides of the paper, with a twist.
32   Onvacation   2021 Aug 21, 8:41pm  

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

Not all problems have solutions, but this one does.
33   Onvacation   2021 Aug 21, 8:42pm  

And it's not Komputodos
34   Onvacation   2021 Aug 21, 8:44pm  

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.
35   qroproton   2021 Aug 21, 8:46pm  

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

Hell! You are right.
36   Tenpoundbass   2021 Aug 22, 11:41am  

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.
37   Tenpoundbass   2021 Aug 22, 11:46am  

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?
38   Tenpoundbass   2021 Aug 22, 11:48am  

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.
39   GNL   2021 Aug 22, 12:03pm  

When do we get to see the solution?
40   richwicks   2021 Aug 22, 12:05pm  

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.

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