Thank you
Heya codemaster3001…
Yep. Still waiting for your teacher’s solution to the OP problem… innocent blink
heheh
-Sweep
I’ve seen this question posted here and on other news groups numerous times. My favorite is when they include a link to a jpg of the puzzle and you can clearly see all of the half erased pencil marks from their failed attempts.
Haj
Is the teacher perhaps expecting someone to point out that it is easily possible in three dimensions?
commasense, you’re thinking of a different problem - I must admit that I thought that’s the one this post was about at first, too!
The one you’re thinking of has nine dots arranged in a 3x3 grid:
O O O
O O O
O O O
and the problem is to draw three straight lines, without lifting the pen from the paper, such that they pass through all nine dots. (The simpler problem is to draw four such lines, for which the solution is as follows:
O-O-O-
|\ /
O O O
| X
O O O
|/
Sorry for the cruddy drawing - you start at the top left and go across the top, then down diagonally left, then up, then down diagonally right.)
The answer for three lines uses the fact that the dots have dimensions, as you point out, so you can draw a figure like this:
_
O O-O
>
O-O-O
<
O-O_O
if you can imagine that those weird symbols form a straight line…
I’m still looking forward to hearing the teacher’s “solution”, though.
As mentioned above, you can do it on a donut. So you can do it on a piece of paper if you make a hole in the paper. Would that count? Probably not.
If you want to cheat, make the dots with a big fat black magic marker so the dots show up on both sides of the paper. Then it’s easy. Of course that isn’t going count either. Sigh.
If you draw it on the torus (doughnut), how do you do it. I went to some site but they had the houses and utilities intermixed. If the houses are on one side and the utilites are on the other can you do it even on the doughnut?
It doesn’t matter where the houses and utilities are located.
if it doesn’t matter then how come i can figure out how to do it if they’re on opposite sides?
If it doesn’t matter then how come i can’t figure out how to do it if they’re on opposite sides?
sorry about that.
You must have a mistake or you cheated. K[sub]3,3[/sub] was proven long ago to not be embedable in the plane.
Actually, there IS a solution to the problem as stated, but it involves either lateral thinking, or cheating, depending on your point of view.
The question is usually stated in terms of three houses and three utility companies, each utility company has to supply each house. It is possible IF you permit a company to reach a house by passing through another house.
I can’t reproduce the diagram in ascii, so I’ll describe it carefully.
A B C
1 2 3
i) Straight line from A, linking to 1
ii) Straight line from A, linking to 2
iii) Straight line from B, linking to 2
iv) Straight line from B, linking to 3
v) Straight line from C, linking to 3
vi) Line from B, passing around A, linking to 1
vii) Line from C, passing around 3, linking to 2
viii) Line from C, passing around 3, linking to 1
and the tricky one …
ix) Line from A passing through 2, linking to 3
Hey Cabbage, that is not a moebius signature. It is a cylindrical signature at best. A moebius sig would come back upside down.
Yeah, I know that. But it was given to me by WallyM7 (rest his soul), and I still think it’s pretty cool. I don’t think it would sound as cool if I changed it to “This is a circular/cylindrical sig”.
I haven’t seen it in a while, but someone (can’t remember who) here has (or had) a genuine (more or less) moebius sig (the upside down part was done with regular characters that looked similar to the upside down letters, but I can’t remember what characters were used, exactly).
You never told us your architecture teacher’s “solution.” What did he/she say?
My previous post says it all. I won’t blow the tanks on this again–I’m just curious.