Preserved Topic: Image puzzle (Page 1 of 1)

Ok, there are three boxes arranged in a pyramid, like so:



You have to draw a continuous line and cross every line segment in the pyramid shape, without crossing any line segment twice. Wrong examples can be seen below (what's wrong with them is circled in a different color). You CAN cross your own line, but you may not cross any line segment twice.




I've been working on this puzzle for a few years now. I refuse to think that there is no solution... but I could be wrong Click for psd.

========================
Of course you're entitled to your own opinion.
Who said I have to agree with it?

[This message has been edited by Raptor (edited 01-14-2002).]

You CAN cross your own line??? please explain!

The yellow line, aka the one that you draw. You can cross that if you like, but you can't cross any line segments of the boxes more than once. *goes and makes an example*



The part circled in red is allowed.

========================
Of course you're entitled to your own opinion.
Who said I have to agree with it?

[This message has been edited by Raptor (edited 01-13-2002).]

#1: You didn't cross all the lines

#2: You crossed one of them twice.

i know the solution is for you to figure out

========================
Of course you're entitled to your own opinion.
Who said I have to agree with it?

I... HATE YOU.... now... getting that aside... I still HATE YOU...

AHHHHHHH.. ~runs away screaming~ I am never gonna have time to learn Raptor! ~Vp~

It's impossible. I've explained why a few times, but I'm not in the mood right now.

unless you show me the answer... there is none. I agree wit mage... I cant believe how much time i waisted on that.

I'm going to go out on a limb and claim that there's no solution. Here's why...

To simplify things, I drew a line segment in each line that will have to be gone through eventually:



Now all I have to do is join the line-segments that I've created.

So, then I realized that in *each* box, there are five line-segment-endings (yellow). You can connect one pair, and then you can connect another pair, but you will *always* have one line-segment-ending left in each box (since there are five in each box, there will always be an odd one left out). Since there are three boxes, and each one will have at least one line-segment-ending left over, there must be three ends to the final line that we're going to draw. Since no continuous line can have three ends, I believe there is no solution.

...or did I overlook something?

(oh... apparently I'm not going out on a limb... posts have been made since I started working on the puzzle)

that would be the so-called "Königsberger Brückenproblem" by good ol Leonhard Euler.
it's all graphical kombinatorics. i did an exam on that last october.

I had a problem like this when I was at school. The answer turned out to be that you had to draw the problem on a rubber ring so you could actually draw lines around the back of the ring to reach parts of the puzzle without technically crossing lines. I wonder if that solution would work here.....

~goes off to find a rubber ring~

Morph, Forget the ring.
That ought to work out just as well by putting the lines in a new layer

Heh. Not bad, Slime.

My approach to explaining it is the inside/outside approach.

Even number polygon -- if you start on the outside, then you end up on the outside. If you start on the inside, then you end up on the inside.

Odd number polygon -- if you start on the outside, then you end up on the inside. If you start on the inside, then you end up on the outside.

Since you have 3 odd polygons, no matter where yous start (inside or outside any of the polygons), you have to end up inside 2 of the polygons.

Works better with draw examples, but that's the jyst of it.

I've been having dreams... bad bad bad dreams....since this was posted because it was familiar. I used to have several books on 'Tricks' trick questions..magic etc...and this is a 'trick question.' it's in one of those books. Those books are still packed and it will be a while yet before they're unpacked so I'm going from a foggy memory but I think you'll get the idea.

It's all in how the question is 'worded.' It says you must cross the lines only once...as in Slime's example...and that you can cross your own lines as many times as you like.

What the question *does not* say is that you can or cannot "travel" down a line. When you consider it from that perspective... this is the solution. For sure it is a 'trick question'

So which is it... don't believe me... or mad that it's a trick question?

the first "error" raptor mentioned, could well be the solution. since "lines" have no real thickness, all we have to do is touch them =P
so.... in the error part, all we have to do is imagine a curve that only touches the line above in one point ^-^

good going nojive

No one said the lines had to be on a two dimensional surface, either. Oh, and we could make a line that travels back in time to before the bricks were drawn, and then back forward in time, so it can move anywhere without actually crossing any lines!

=)

I'm <LOL> Slime!

I had/have a slew if books with these sort of 'trick questions.' Great fun and very frustrating.

Was kinda funny... when the puzzle was posted all I could see in my minds eye... were spirals and loop type things...and days later.... DOWN THE LINE! Anyway...

nj

Well done, NoJive!!! I want to share this scene with you concerning the Kobayashi Maru:

__________________________________________
SAAVIK On the test, sir. Will you tell me what you did? I would really like to know.

Kirk looks at Bones, who smiles -

BONES Lieutenant, you are looking at the only Starfleet cadet who ever beat the no-win scenario -

SAAVIK How?

KIRK I reprogrammed the simulation so it was possible to rescue the ship.

SAAVIK WHAT?

DAVID (laughs) He cheated!

KIRK I changed the conditions of the test. I got a commendation for original thinking.

(pause)

I don't like to lose.

SAAVIK Then - you never faced that situation - faced death...

He picks up the communicator.

KIRK I don't believe in the no-win scenario.
__________________________________________

On behalf of StarFleet Academy, I would like to give you a commendation too! LOL!!!

Thanx Bugs It really was a complete and total hooot! There I was on the bed looking up at the grid work in the ceiling *trying* to explain (using the grid-finger- pointing-method ) to my "I'm sleeping now" wife.... this puzzle... "I know this! I know this!! <lolbt>

I have at least one more "visual condunrdum" which I hope to post before my f2s... goes south... stay tuned

nj