Comments on: It's been 24 years. I give up.

Question: It's been 24 years. I give up.

mecran01 — Sun, 06 Jan 2008 20:03:06 -0800

My geometry teacher in high school in 1984 showed us this puzzle. I was only half paying attention, but I believe the goal was to draw a line that intersected each segment only once.

I was only half paying attention, but I believe the goal was to draw a line that intersected each segment only once. The line you drew could intersect itself. I have been doodling with this thing, off and on for 24 years.

Does anyone know the origin of this puzzle? I saw it in an IQ test. AFAIK, the solution, if there is one, has something to do with drawing a line that crosses the point(s) where two different segments meet, and there being some sort of indeterminacy about whether the line one drew intersected one point or another.

Anyway, I'm giving up. I need closure.

Mr. Farrer, who taught at Alta High School in Sandy, Utah: you win, and I apologize for not paying closer attention.

By: knowles

knowles — Sun, 06 Jan 2008 20:06:44 -0800

unpossible.

By: knowles

knowles — Sun, 06 Jan 2008 20:09:00 -0800

and a wiki link.

By: gursky

gursky — Sun, 06 Jan 2008 20:09:11 -0800

after struggling with the same puzzle for a few weeks, i sent it to my brother.

my brother said it was impossible.

By: gursky

gursky — Sun, 06 Jan 2008 20:09:27 -0800

(my brother is a genius)

By: mecran01

mecran01 — Sun, 06 Jan 2008 20:14:23 -0800

Here is a more detailed discussion of the same class of problems:

Seven Bridges of Konigsberg.

This is going to sound weird, but I feel like crying right now.

By: krisjohn

krisjohn — Sun, 06 Jan 2008 20:17:36 -0800

How thick can the line be?

By: knowles

knowles — Sun, 06 Jan 2008 20:18:44 -0800

we can all learn a valuable lesson here:

paying attenention in school gets you nothing.

By: mecran01

mecran01 — Sun, 06 Jan 2008 20:21:18 -0800

Ah, I hadn't considered line thickness. I guess you could make the line thicker than the actual diagram, although I assumed it had to be the same thickness as the lines composing the original figure. I guess I need to go read some graph theory.

By: stereo

stereo — Sun, 06 Jan 2008 20:25:57 -0800

Possible

By: Korou

Korou — Sun, 06 Jan 2008 21:05:52 -0800

I don't think a line has thickness.

By: explosion

explosion — Sun, 06 Jan 2008 21:08:04 -0800

stereo, that "solution" you link to has the line going through the corners, not through the walls. It's not so much clever as avoiding answering the question by rephrasing it. Kind of like when Calvin in Calvin & Hobbes wrote an essay in gibberish because it said, "Answer in your own words".

By: Steven C. Den Beste

Steven C. Den Beste — Sun, 06 Jan 2008 21:53:05 -0800

The solution I remember seeing when I was a kid had the drawn line running along the middle of the top center line, from one end of it all the way to the other. Like this.

But there's no way to solve it without cheating.

By: thebrokenmuse

thebrokenmuse — Mon, 07 Jan 2008 20:32:27 -0800

The first thought I had was what Steven C. suggested. I am terrible at math though, so maybe I misunderstood the question.

By: mecran01

mecran01 — Fri, 11 Jan 2008 09:33:30 -0800

More discussion via Stereo's link above. FWIW I already came up with the idea of drawing through the point of intersection, but that's cheating. The fat line method never occurred to me, nor did solving the problem in three dimensions.

By: mdn

mdn — Sun, 16 Nov 2008 22:35:16 -0800

The solution I remember seeing when I was a kid had the drawn line running along the middle of the top center line, from one end of it all the way to the other. Like this.

Hm, but that then intersects the lower middle rectangle's upper wall twice - in fact wouldn't it make more sense to skip the cheat altogether and just have the last line go straight through the middle wall? Then you have a spiral that starts on the outside and ends on the inside, like the logical "answer" says it has to, but which seems to intersect each wall... ?