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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5$\begingroup$ 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 OCommented May 3, 2015 at 6:34
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2$\begingroup$ 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 OCommented May 3, 2015 at 6:35
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$\begingroup$ I feel like I've seen this on this site before, but can't find it. $\endgroup$– SpencerkattyCommented May 3, 2015 at 16:05
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3 Answers
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Is it valid that 2 of the corners are beyond the stars?
Here's my attempt!
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4$\begingroup$ This is the most common answer to this children's puzzle. $\endgroup$ Commented May 3, 2015 at 9:42
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I've never seen this one before, but here's what jumps out at me:
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$\begingroup$ 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. $\endgroup$ Commented May 3, 2015 at 7:45
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2$\begingroup$ Doesn't the second one not pass through the leftmost star? $\endgroup$– user10203Commented May 3, 2015 at 8:06
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$\begingroup$ @Reticality It does look that way, doesn't it? scratches head $\endgroup$– CalebCommented May 3, 2015 at 8:10
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$\begingroup$ It just might work in Lobachevskian geometry. $\endgroup$– CalebCommented May 3, 2015 at 8:18
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$\begingroup$ 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.) $\endgroup$– egmontCommented May 3, 2015 at 10:27
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Using the information from http://en.wikipedia.org/wiki/Parallel_(geometry)#Extension_to_non-Euclidean_geometry:
- 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:
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.