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57
Onvacation
2021 Aug 22, 4:15pm
Onvacation
2021 Aug 22, 4:15pm
Tenpoundbass says
Theoretically.
If you know all of the stupid shit you shouldn't do, then you're only left with all of the sensible options.
Theoretically.
59
richwicks
2021 Aug 22, 7:11pm
richwicks
2021 Aug 22, 7:11pm
Onvacation says
Demonstrate it.
Going to the back of the paper does not solve the problem. Lines cross on the back of the paper.
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.
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.
Demonstrate it.
Going to the back of the paper does not solve the problem. Lines cross on the back of the paper.
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.
60
Onvacation
2021 Aug 22, 7:22pm
Onvacation
2021 Aug 22, 7:22pm
richwicks says
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.
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.
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.
61
richwicks
2021 Aug 22, 7:32pm
richwicks
2021 Aug 22, 7:32pm
Onvacation says
We'll meet up. I'm curious as to the divergence between my generation and your generation, and generation Y.
I think the "generation gap" is about how we've been propagandized differently. I THINK I'm outside of that sphere however, I've thought that before to realize I was not. The generation gap is imposed upon us, top down, it's not natural.
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.
We'll meet up. I'm curious as to the divergence between my generation and your generation, and generation Y.
I think the "generation gap" is about how we've been propagandized differently. I THINK I'm outside of that sphere however, I've thought that before to realize I was not. The generation gap is imposed upon us, top down, it's not natural.
62
Patrick
2021 Aug 22, 10:37pm
Patrick
2021 Aug 22, 10:37pm
Onvacation says
I'd be up for that too.
@richwicks Looking forward to meeting up with you in person again one of these days.
I'd be up for that too.
63
GreaterNYCDude
2021 Aug 23, 6:20am
Patrick says
I think we're long overdue for some sort of PatNet meetup.
Onvacation 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.
64
FortwayeAsFuckJoeBiden
2021 Aug 23, 6:44am
GreaterNYCDude says
We need some closer to LA.
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.
We need some closer to LA.
65
komputodo
2021 Aug 23, 9:44am
komputodo
2021 Aug 23, 9:44am
well if we are looking at the theoretical solutions, why not sett up the electricity with a wireless transmission system? lol
66
komputodo
2021 Aug 23, 9:46am
komputodo
2021 Aug 23, 9:46am
for all of the gang that likes puzzles, have you ever tried to explain the MONTY HALL PROBLEM to anyone? It can get frustrating and hilarious.
67
mell
2021 Aug 23, 9:53am
komputodo says
It's still my favorite one because it took me a while to grapple - of course the math clearly shows the 2/3 to 1/3 probability ratio after one door has been opened (by the game master in the know that the prize is not behind the door they chose top open) but the brain has a hard time to accept it. Many people won't believe it, but it's easier explained if you start with 1000 doors.
for all of the gang that likes puzzles, have you ever tried to explain the MONTY HALL PROBLEM to anyone? It can get frustrating and hilarious.
It's still my favorite one because it took me a while to grapple - of course the math clearly shows the 2/3 to 1/3 probability ratio after one door has been opened (by the game master in the know that the prize is not behind the door they chose top open) but the brain has a hard time to accept it. Many people won't believe it, but it's easier explained if you start with 1000 doors.
68
Tenpoundbass
2021 Aug 23, 10:59am
Tenpoundbass
2021 Aug 23, 10:59am
richwicks says
Onvacation saysTenpoundbass 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.
Demonstrate it.
70
Onvacation
2021 Aug 23, 2:22pm
Onvacation
2021 Aug 23, 2:22pm
One of Mr. Schultz's constraints was you could not go through the paper.
From: https://www.archimedes-lab.org/How_to_Solve/Water_gas.html
The only way to solve this problem that I know of is to twist the paper into a moebius strip. Technically doing this turns the two dimensional paper into a three dimensional geometric shape, albeit a strange one with one side and one edge.
From: https://www.archimedes-lab.org/How_to_Solve/Water_gas.html
*Category:* Topological graph theory.
*Name:* Water Gas and Electricity puzzle, Three Utilities puzzle, or Three Cottage problem.
*Material:* Pencil, piece of paper.
*Configuration:* There are three houses (or squares) drawn on paper and below them three smaller squares [or circles] representing gas, water, and electricity suppliers.
*Aim of the game:* Draw lines to get each utility into every house, without crossing over any line.
*Origin of the puzzle:* Unknown. Sam Loyd claimed that he invented this recreational math problem about 1903. But this puzzle is MUCH older than electric lighting or even gas, Loyd most probably modified a previously existing puzzle.
*Editor's notice:* This is a pure abstract mathematical puzzle that imposes constraints that would not be issues in a practical engineering scenario... As such, this puzzle CANNOT be solved.
The only way to solve this problem that I know of is to twist the paper into a moebius strip. Technically doing this turns the two dimensional paper into a three dimensional geometric shape, albeit a strange one with one side and one edge.
71
Onvacation
2021 Aug 23, 2:28pm
Onvacation
2021 Aug 23, 2:28pm
I remembered this problem because an easy way to create graphs with Excel came to me in a dream.
The solution to the "water/gas/electricity" problem came to me in a dream after I studied graph theory and topology when I was a math major in college.
Dreams are cool!
The solution to the "water/gas/electricity" problem came to me in a dream after I studied graph theory and topology when I was a math major in college.
Dreams are cool!
72
komputodo
2021 Aug 23, 10:28pm
komputodo
2021 Aug 23, 10:28pm
Onvacation says
Then why set it up as 3 houses with gas, elec, and water meters? why not just 3 circles and three squares?
*Editor's notice:* This is a pure abstract mathematical puzzle that imposes constraints that would not be issues in a practical engineering scenario... As such, this puzzle CANNOT be solved.
Then why set it up as 3 houses with gas, elec, and water meters? why not just 3 circles and three squares?
73
komputodo
2021 Aug 23, 10:30pm
komputodo
2021 Aug 23, 10:30pm
mell says
Would the odds change if the player instead of Monty opened the door(s) randomly with 1000 doors and just by sheer coincidence just happened to leave 1 winner and 1 loser?
It's still my favorite one because it took me a while to grapple - of course the math clearly shows the 2/3 to 1/3 probability ratio after one door has been opened (by the game master in the know that the prize is not behind the door they chose top open) but the brain has a hard time to accept it. Many people won't believe it, but it's easier explained if you start with 1000 doors.
Would the odds change if the player instead of Monty opened the door(s) randomly with 1000 doors and just by sheer coincidence just happened to leave 1 winner and 1 loser?
74
Onvacation
2021 Aug 23, 10:36pm
Onvacation
2021 Aug 23, 10:36pm
komputodo says
For the same reason they don't explicitly teach second graders negative numbers. Graph theory is a little too abstract for ninth graders.
Math is often years ahead of technology, sometimes centuries. If E=MC^2, M=E/C^2; try wrapping your brain around that. The mathematical field of topology explains wormholes and theoretically explains the possibility of faster than light travel, though I don't even pretend to understand how.
Then why set it up as 3 houses with gas, elec, and water meters? why not just 3 circles and three squares?
For the same reason they don't explicitly teach second graders negative numbers. Graph theory is a little too abstract for ninth graders.
Math is often years ahead of technology, sometimes centuries. If E=MC^2, M=E/C^2; try wrapping your brain around that. The mathematical field of topology explains wormholes and theoretically explains the possibility of faster than light travel, though I don't even pretend to understand how.
75
SunnyvaleCA
2021 Aug 23, 10:52pm
I once twisted the insides of a floppy disk into a Möbius strip and hung it on my cubical wall with the label: single-sided floppy disk. That got a chuckle from co-workers.
76
Tenpoundbass
2021 Aug 24, 9:32am
Tenpoundbass
2021 Aug 24, 9:32am
Onvacation says
That's where math fails the Eggheads. Just because math fits a scenario, sometimes it is completely useless outside of those bounds.
A great example is Time. Out depiction of time through a math system of 12 values with 60 segments, parsed in 24 hour dimensions, spread out over 365 Days, among many time zones, has absolutely no value anywhere else in the cosmos, other than to explain our planets rotation around the sun. And it's sloppy at best, and has to be reworked periodically, with subtractions here and there.
It's possible that a wormhole only works on paper, and has no value in the Universe.
The mathematical field of topology explains wormholes and theoretically explains the possibility of faster than light travel, though I don't even pretend to understand how.
That's where math fails the Eggheads. Just because math fits a scenario, sometimes it is completely useless outside of those bounds.
A great example is Time. Out depiction of time through a math system of 12 values with 60 segments, parsed in 24 hour dimensions, spread out over 365 Days, among many time zones, has absolutely no value anywhere else in the cosmos, other than to explain our planets rotation around the sun. And it's sloppy at best, and has to be reworked periodically, with subtractions here and there.
It's possible that a wormhole only works on paper, and has no value in the Universe.
77
mell
2021 Aug 24, 9:34am
Onvacation says
There are other ways to achieve faster than light travel that are less esoteric such as riding inside a gravitational wave while having your own propulsion adding to the total speed. Just sayin ;)
komputodo saysThen why set it up as 3 houses with gas, elec, and water meters? why not just 3 circles and three squares?
For the same reason they don't explicitly teach second graders negative numbers. Graph theory is a little too abstract for ninth graders.
Math is often years ahead of technology, sometimes centuries. If E=MC^2, M=E/C^2; try wrapping your brain around that. The mathematical field of topology explains wormholes and theoretically explains the possibility of faster than light travel, though I don't even pretend to understand how.
There are other ways to achieve faster than light travel that are less esoteric such as riding inside a gravitational wave while having your own propulsion adding to the total speed. Just sayin ;)
« First « Previous Comments 57 - 77 of 77 Search these comments
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?