patrick.net
An Antidote to Corporate Media
1,198,929 comments by 14,158 users - desertguy, ForcedTQ, Patrick, PeopleUnited, stereotomy online now
invite response« First « Previous Comments 70 - 77 of 77 Search these comments
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 70 - 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?