25 Dots, 8 Lines

http://e-riddles.blogspot.gr/2013/04/25-dots-8-lines.html

by hliaskal • 13 years ago

25 24 13 years ago

e-riddles.blogspot.gr

TranceMan• 13 years ago

Spoiler - interesting solution [from the comments]: http://www.scribd.com/doc/133494020/Extended-9-dots-puzzle-t...

Solved mathematically :)

Someone2• 13 years ago

Where's the 'solved' part? At the very best, he shows that you can do it with 2n-2 lines. Even that includes a lot of hand waving/implicit "it is easy to see"-s.

That you need 2n-2 lines, he doesn't talk about at all.

danbruc• 13 years ago

Additionally the OEIS now contains a wrong fact [1] - the sequences are offset by one. I am not even convinced that 2n - 2 is optimal - does somebody know if it is or can proof a better lower bound than the trivial n?

[1] http://oeis.org/A058992

kaoD4• 13 years ago

I can solve it with just 5 lines. You just have to get the pen to infinity and then come back.

Wait, if infinity wraps around that'll take just one line!

eCa• 13 years ago

What if you wrap the paper (if the dots are on paper) and draw a line round-and-round?

A bit hard to ensure that it's straight though..

kaoD4• 13 years ago

Who needs paper when you have ℝ²? :P

bcoates• 13 years ago

It doesn't say you have to go through the center of the dot. If you angle them a bit 5 non-infinite lines will do.

kaoD4• 13 years ago

My technical drawing teacher called that the "fat point theorem".

DrStalker• 13 years ago

It doesn't have to go to infinity.

Look at this solution for 9 dots/three lines: http://www.goodmorningcreativity.com/wp-content/uploads/2010...

That scales up to whatever sized square of dots you like, provided the "dots" are not points but are circles with a non-zero diameter.

yk3• 13 years ago

I am pretty sure that it is meant to be solved on a compact, simple connected subset of |R^2, with Euclidean metric.

S4M• 13 years ago

Careful with that. If the frontier of that subset is not far enough from the points, the problem will not be solvable.

kaoD4• 13 years ago

I'm pretty sure I was just joking.

Strilanc• 13 years ago

Solution (rot13):

Whfg genpr nebhaq gur bhgfvqr gura hfr gur fbyhgvba gb gur fznyyre chmmyr.

pdevr• 13 years ago

Great. Keeps it simple.

On a side note, can anyone build a cool ROT13 converter? There are some, but they are showing their age.

petterjohnson• 13 years ago

What? kindly explain a little..

twiceaday• 13 years ago

My solution: http://i.imgur.com/z2mo2Jj.jpg

tydok• 13 years ago

My solution http://i.imgur.com/S2L9pht.jpg

panacea• 13 years ago

It doesn't specify that you can't add curved lines between your straight lines without lifting your pen.

frooxie• 13 years ago

It's possible to solve it entirely "within" the box.

mdellabitta• 13 years ago

Why do you need 8 lines? You just need 5 lines, and an enormous piece of paper.

EDIT: Beaten to the punch. I should learn to read comments first.

mkl• 13 years ago

I left a hill-climbing solver running overnight and found quite a few solutions, including a couple that can be made to stay inside the square: http://imgur.com/a/Wd2dS

25 Dots, 8 Lines

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