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Also: https://www.archimedes-lab.org/How_to_Solve/Water_gas.html
The rules say you can't cross any lines, houses and utilities included.
Is there a line crossed?
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 saysI 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.
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!
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
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.
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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?