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        riddles >> hard >> 16 lines
        
(Message started by: eN on Oct 28^th, 2004, 3:01am)

Title: 16 lines
Post by eN on Oct 28^th, 2004, 3:01am

Anyone do this one?

you have to draw one line through all the lines once, theres 16 lines.

eN

Title: Re: 16 lines
Post by Barukh on Oct 28^th, 2004, 4:29am

eN, your formulation is a bit cryptic. Can you make more clear?

Despite this, I tried to guess what was the question, and I doubt [hide]the solution is possible[/hide].

Title: Re: 16 lines
Post by TimK on Oct 28^th, 2004, 5:05am

I think it's the same problem as trying to trace the figure below without picking up your pencil, and without tracing the same line twice - it's impossible.

Title: Re: 16 lines
Post by THUDandBLUNDER on Oct 28^th, 2004, 7:05am

I remember wasting hours on this one when I was a little kid.

on 10/28/04 at 05:05:37, TimK wrote:

it's impossible.

...and yet not very Hard. :)

Title: Re: 16 lines
Post by John_Gaughan on Oct 28^th, 2004, 7:57am

on 10/28/04 at 07:05:31, THUDandBLUNDER wrote:

I remember wasting hours on this one when I was a little kid.

...and yet not very Hard. :)

Of course, children have a unique way of solving problems. Some might call it naive, some might call it creative. I think that by [hide]folding the paper[/hide] one could draw a line intersecting all of those lines.

Title: Re: 16 lines
Post by eN on Oct 31^st, 2004, 3:55am

ok ok ok yeah this ones a bitch! ok you can only draw one like through these 16 lines but you cant go through the same once twice

i.e.

Title: Re: 16 lines
Post by Icarus on Oct 31^st, 2004, 5:56am

A basic and well-known result in graph-theory shows that by ordinary interpretation, this is impossible. The picture shows 6 regions (the 5 rectangles + the outside). These regions have 5,5,4,5,4 and 9 "sides" respectively. Each time the curve enters a region and leaves, it removes two sides from those still needing intersected. Because the sides are intersected in pairs, every region - except those the curve begins and ends in - must have an even number of sides for every side to be intersected. Thus, any puzzle like this can have only two regions with an odd number of sides if it is to be solvable. This picture has 4 regions and so cannot be solved.

That said, whoever gave you the puzzle will almost certainly tell you there IS a solution. The trick is, he or she is NOT giving the instructions the "ordinary" interpretation. A minor change in your graph above will "intersect" the missing side, and also close the curve into a loop.

Title: Re: 16 lines
Post by Grimbal on Nov 2^nd, 2004, 3:41am

It depends what you mean by "going through a line" ;D

Title: Re: 16 lines
Post by THUDandBLUNDER on Nov 2^nd, 2004, 3:49am

on 10/28/04 at 03:01:22, eN wrote:

you have to draw one line through all the lines once...

...and also on what he means by once? ::)

Title: Re: 16 lines
Post by eN on Nov 2^nd, 2004, 6:09am

im pretty sure it can be done just need some clever way :D and no you cant go through the line like "Grimble" did and yes just one line one try simple as that.

eN`

Title: Re: 16 lines
Post by TimK on Nov 2^nd, 2004, 6:46am

Let's see it, Icarus

Title: Re: 16 lines
Post by Grimbal on Nov 2^nd, 2004, 8:07am

Hm... either there is no solution or there is a catch.

Do you mind telling us where the 16 lines are, exactly?

And can we assume that the thickness of the additional line is conceptually zero and does not, for instance, exceed the size of the whole figure?

And can we cross from one rectange to the other through the meeting point of 3 lines without couning as "crossing a line"?

Title: Re: 16 lines
Post by THUDandBLUNDER on Nov 2^nd, 2004, 8:13am

Quote:

Do you mind telling us where the 16 lines are, exactly?

Each side of a rectangle has been counted as a separate line.
Thus the perimeter consists of nine lines.

Title: Re: 16 lines
Post by Grimbal on Nov 2^nd, 2004, 8:15am

on 11/02/04 at 08:13:01, THUDandBLUNDER wrote:

Each side of a rectangle has been counted as a separate line.
Thus the perimeter consists of nine lines.

That is your interpretation. Is it also eN's?

Title: Re: 16 lines
Post by Icarus on Nov 3^rd, 2004, 8:01pm

on 11/02/04 at 06:09:46, eN wrote:

im pretty sure it can be done just need some clever way :D and no you cant go through the line like "Grimble" did and yes just one line one try simple as that.

Sorry, but as my argument above clearly shows - there is NO way unless you twist the interpretation as Grimbal has done.

on 11/02/04 at 06:46:47, TimK wrote:

Let's see it, Icarus

You already have. Grimbal's solution is the traditional one for this puzzle. (I have come across this one many times. It even exists elsewhere on this site, I believe.)

on 11/02/04 at 08:15:29, Grimbal wrote:

That is your interpretation. Is it also eN's?

It's the interpretation he himself uses in reply #5.

Title: Re: 16 lines
Post by TimK on Nov 4^th, 2004, 4:47am

Ah, I didn't notice that the segment at the top goes along the line. That's pretty slick.