Take the 2-minute tour ×
Puzzling Stack Exchange is a question and answer site for those who study the creation and solving of puzzles. It's 100% free, no registration required.

in the picture below can you draw 6 straight lines that passes all the circles?
as soon as you start drawing lines you can't take your pen up until you draw all six lines.
hint: you don't have to keep the polyline inside the square

enter image description here

share|improve this question
1  
hint: you don't have to keep the polyline inside the square –  Jan Dvorak Aug 12 at 8:40
    
i knew the answer, if you know that answer it, otherwise i will answer in afew days. –  Riddle Aug 12 at 9:35
1  
Do you have to use all 6 lines? –  RobinvdA Aug 12 at 14:09
    
it is possible with less than 6,but only with 6 lines you can pass the center of each circle.if you can do that with less than 6 do it in answer. –  Riddle Aug 12 at 15:54

13 Answers 13

up vote 30 down vote accepted

I think this is one possible solution:

enter image description here

share|improve this answer

Here's an option that uses only 4 lines. You can extend the concept to place another 2 lines if you really want 6 ...

using 4 lines

share|improve this answer
7  
This is what I immediately thought of when I read the question. +1. This works for arbitrarily small circles, since the lines can be arbitrarily long. And if you give me 0-size circles, I can still do it with infinitely long lines! –  Cruncher Aug 12 at 14:35
2  
it is possible with less than 6,but only with 6 lines you can pass the center of each circle, which i didn't mention in this puzzle.but still your answer is correct.can you pass center of each line with less than 6 lines? –  Riddle Aug 12 at 15:56
3  
@Riddle well that would be the same as passing through 0-size circles which works with infinitely long lines as Cruncher mentioned in his/her comment. –  ExpectoPatronum Aug 13 at 9:03
1  
... and whether you can draw two parallel lines without lifting your pen depends on whether they meet, which in turn depends on the geometry of the space in which the figure appears. Paste the figure to a torus (at an angle) and you can do it in one line! –  user1501 Aug 13 at 12:32
    
@ExpectoPatronum I guess the crux is that you can't draw infinitely long lines :) –  Cruncher Aug 15 at 20:54

If you use just one massive line, you can make it pass through the center of all of the circles!

enter image description here

share|improve this answer
    
that's not what i meant, and what kind of pen is it?it's just a big triangle not big line. –  Riddle Aug 12 at 19:36
18  
It's just a really big pen. It is not a triangle. –  waylon531 Aug 12 at 19:56
18  
+1 trollarious - –  bamboon Aug 13 at 8:46
9  
I signed up to +1 this. Hilarious! regarding it being a square and not a line, just extend the 'line' very far beyond the border and zoom out. problem solved, you have a line that looks like a line. –  n00b Aug 13 at 20:00
1  
aahahha that made my day... –  N0ir Aug 13 at 22:27

By mapping the puzzle onto a cylindrical topography, I've solved the puzzle using only a single straight line.

enter image description here

enter image description here

share|improve this answer
    
it is possible with less than 6,but only with 6 lines you can pass the center of each circle, which i didn't mention in this puzzle.but still your answer is correct.can you pass center of each line with less than 6 lines? –  Riddle Aug 12 at 15:57
9  
Why have the sides match up evenly? Have the right side of the first row of circles match up with the left side of the second row of circles, and your line should go through the center of all the circles. –  Rob Watts Aug 12 at 20:19
    
How to create this image? –  justhalf Aug 13 at 6:07
3  
What definition of straight line are you using here? Presumably something other than "shortest path between two points"? –  jl6 Aug 14 at 12:40
2  
@justhalf, that was created in Sketchup with the puzzle image mapped onto a cylinder as a texture (I have the joy of being Simon's boss) –  Caius Jard Sep 18 at 14:53

enter image description here

Here's another way of thinking. This is using edges instead.

share|improve this answer
    
I like this one a lot. –  jliv902 Aug 13 at 19:27
    
This actually looks like art :) +1, I would hang this –  Cruncher Aug 15 at 20:59
  1. Print the picture.
  2. Fold the image such that there is a single stack of circles. This will take 6 folds.
  3. Draw one line across the middle of it.
  4. Profit.

enter image description here

share|improve this answer
    
actually you just draw a line on one of circles, if you unfold your paper again just one of them has been crossed, it seems you just disappeared the other circles. –  Riddle Aug 13 at 7:23
5  
+1 for "Profit"! –  CJ Dennis Aug 13 at 9:04
3  
@Riddle: It's all about point of view. From my point of view the line has crossed the center point of all of the circles as they are stacked on top of each other. The problem with this exercise is that you haven't defined any real boundary conditions (things you are explicitly not allowed to do). This means there are many different ways of solving the puzzle that don't fit your preconception. –  Chris Lively Aug 13 at 14:10
4  
Just set the point of the pen on the center of the circle and push really hard with the pen, then it will have passed through all the circles. It is one line, going through the z-axis of the folded paper. –  Anssssss Aug 15 at 21:18
    
@Anssssss: that's even better! –  Chris Lively Aug 15 at 22:42

This one doesn't solve it the way your supposed to, but also doesn't break any of the implied "rules", but kind of defeats the purpose of the puzzle (which is go outside of the square). Were you to make the circles smaller, it would eliminate this answer from plausibility. (Also the (3,3) circle line is a little dubious, if I had taken some more time to perfect this it would fit inside the circle better, but also shows how this solution could be easily invalidated by making the circles smaller)

enter image description here

share|improve this answer
1  
You better write that this way you manage to keep the polyline inside the square! +1 –  klm123 Aug 12 at 17:33
    
You can move the vertex at (1,2) upwards slightly to get a better fit for (3,3) up to the point where it equals the fit for (3,2). –  Jan Dvorak Aug 13 at 18:15
    
Yeah, I didn't try super hard to get it to fit perfectly, as it kind of helped point out how this method is easily broken by making the circles smaller. –  DLeh Aug 13 at 18:27

Why not this?

This one also does what he wants.

share|improve this answer
2  
because you take your pen up for several times –  Riddle Aug 13 at 7:19
3  
@Riddle But if we r allowed to trace back our path then its doable this way without lifting the pen right. –  Hubble07 Aug 13 at 8:27
    
No, check out in my own answer it is drawn with 6 lines and the pen didn't lift up –  Riddle Aug 13 at 8:49
7  
You don't need to pick your pen up. Just double back on the line you already drew. –  Roddy of the Frozen Peas Aug 14 at 1:49
4  
Wouldn't doubling back be drawing another line, though? So you could only have three lines. –  WChargin Aug 14 at 14:42

enter image description here

Similar but different answer. Great puzzle!

share|improve this answer

enter image description here

This could be the answer as well.

6 lines without lifting the pen.

share|improve this answer

an other answer!

here is my answer!

nice question!

share|improve this answer

my own answer to this question is
in this picture you can see 6 lines throw the center of all circles without taking your pen up.

enter image description here

share|improve this answer

Looking through the answers, there are several similar, but none the same as this one. So here's one more possible answer.

Possible answer to the puzzle.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.