enter image description here

Using 4 straight lines connect these 9 stars together without lifting your pen from the surface. The end of each line must be start of the next line.

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    $\begingroup$ This is a fairly standard puzzle, so lots of people will probably already know the answer. If I may make a suggestion - if you do already know at a glance, don't answer, let those who haven't seen it have a proper go at it. $\endgroup$ – Glen O May 3 '15 at 6:34
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    $\begingroup$ And to those who haven't seen this puzzle before, I just thought I'd say that you have to think outside the box to solve it. $\endgroup$ – Glen O May 3 '15 at 6:35
  • $\begingroup$ I feel like I've seen this on this site before, but can't find it. $\endgroup$ – Spencerkatty May 3 '15 at 16:05

Is it valid that 2 of the corners are beyond the stars?

Here's my attempt!


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    $\begingroup$ This is the most common answer to this children's puzzle. $\endgroup$ – Ian MacDonald May 3 '15 at 9:42

I've never seen this one before, but here's what jumps out at me: enter image description here

  • $\begingroup$ I guess, but the "standard" puzzle that Glen references earlier in the comments basically assumes that the lines must pass through the centers of the stars/points/whatever. $\endgroup$ – Dennis Meng May 3 '15 at 7:45
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    $\begingroup$ Doesn't the second one not pass through the leftmost star? $\endgroup$ – user10203 May 3 '15 at 8:06
  • $\begingroup$ @Reticality It does look that way, doesn't it? scratches head $\endgroup$ – Caleb May 3 '15 at 8:10
  • $\begingroup$ It just might work in Lobachevskian geometry. $\endgroup$ – Caleb May 3 '15 at 8:18
  • $\begingroup$ I love your first solution! The puzzle is about "thinking outside the box" (literally:)) and you took it to the next level with just 3 lines, nice! (The second solution is indeed faulty.) $\endgroup$ – egmont May 3 '15 at 10:27

Using the information from http://en.wikipedia.org/wiki/Parallel_(geometry)#Extension_to_non-Euclidean_geometry:

  1. parallel, if they do not intersect in the plane, but have a common limit point at infinity, or [...]

So, if we put this in a non-Euclidean plane, it can be done with one line:

One line

But, of course, this would take forever to draw (But it does pass through the centres of all stars)

I can also confirm it is impossible to do on a Euclidean plane without going outside the box with this Python script.

There are 84 different ways to do it with 5 lines inside the box, but that should be around 11 unique ones because most are reflected or rotated.


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