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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.
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.
*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.
*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.
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.
Then why set it up as 3 houses with gas, elec, and water meters? why not just 3 circles and three squares?
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.
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.
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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?