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Topic: 16 lines (Read 709 times) |
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eN
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Posts: 3
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Anyone do this one?
you have to draw one line through all the lines once, theres 16 lines.
eN
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| « Last Edit: Oct 28th, 2004, 3:02am by eN » |
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Barukh
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Re: 16 lines
« Reply #1 on: Oct 28th, 2004, 4:29am » |
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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 the solution is possible.
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| « Last Edit: Oct 28th, 2004, 4:30am by Barukh » |
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TimK
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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.
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ThudnBlunder
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Re: 16 lines
« Reply #3 on: Oct 28th, 2004, 7:05am » |
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I remember wasting hours on this one when I was a little kid.
on Oct 28th, 2004, 5:05am, TimK wrote:
...and yet not very Hard. 
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John_Gaughan
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Re: 16 lines
« Reply #4 on: Oct 28th, 2004, 7:57am » |
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on Oct 28th, 2004, 7:05am, THUDandBLUNDER wrote:I remember wasting hours on this one when I was a little kid.
...and yet not very Hard. |
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Of course, children have a unique way of solving problems. Some might call it naive, some might call it creative. I think that by folding the paper one could draw a line intersecting all of those lines.
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x = (0x2B | ~0x2B)
x == the_question
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eN
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Posts: 3
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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.
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Icarus
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Re: 16 lines
« Reply #6 on: Oct 31st, 2004, 5:56am » |
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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.
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Grimbal
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It depends what you mean by "going through a line" 
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ThudnBlunder
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Re: 16 lines
« Reply #8 on: Nov 2nd, 2004, 3:49am » |
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on Oct 28th, 2004, 3:01am, eN wrote:
you have to draw one line through all the lines once...
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...and also on what he means by once? 
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eN
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Re: 16 lines
« Reply #9 on: Nov 2nd, 2004, 6:09am » |
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im pretty sure it can be done just need some clever way  and no you cant go through the line like "Grimble" did and yes just one line one try simple as that.
eN`
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TimK
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Re: 16 lines
« Reply #10 on: Nov 2nd, 2004, 6:46am » |
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Let's see it, Icarus
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Grimbal
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Re: 16 lines
« Reply #11 on: Nov 2nd, 2004, 8:07am » |
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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"?
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| « Last Edit: Nov 2nd, 2004, 8:16am by Grimbal » |
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ThudnBlunder
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Re: 16 lines
« Reply #12 on: Nov 2nd, 2004, 8:13am » |
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Quote:| Do you mind telling us where the 16 lines are, exactly? |
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Each side of a rectangle has been counted as a separate line.
Thus the perimeter consists of nine lines.
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Grimbal
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Re: 16 lines
« Reply #13 on: Nov 2nd, 2004, 8:15am » |
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on Nov 2nd, 2004, 8:13am, THUDandBLUNDER wrote:
Each side of a rectangle has been counted as a separate line.
Thus the perimeter consists of nine lines.
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That is your interpretation. Is it also eN's?
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Icarus
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Re: 16 lines
« Reply #14 on: Nov 3rd, 2004, 8:01pm » |
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on Nov 2nd, 2004, 6:09am, eN wrote:| im pretty sure it can be done just need some clever way and no you cant go through the line like "Grimble" did and yes just one line one try simple as that. |
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Sorry, but as my argument above clearly shows - there is NO way unless you twist the interpretation as Grimbal has done.
on Nov 2nd, 2004, 6:46am, TimK wrote:
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 Nov 2nd, 2004, 8:15am, Grimbal wrote:| That is your interpretation. Is it also eN's? |
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It's the interpretation he himself uses in reply #5.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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TimK
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Re: 16 lines
« Reply #15 on: Nov 4th, 2004, 4:47am » |
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Ah, I didn't notice that the segment at the top goes along the line. That's pretty slick.
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