Author 
Topic: HARD: Cigarettes Max Clique (Read 42633 times) 

Nigel_Parsons
Junior Member
Gender:
Posts: 63


Re: HARD: Cigarettes Max Clique
« Reply #25 on: Jun 17^{th}, 2004, 11:19am » 
Quote Modify

'Mathematical Puzzles and Diversions' by Martin Gardner has it as 'The Touching Cigarettes'. with the answer given away by being illustrated on the cover (U.K. edition at least) UK edition is Penguin books ISBN 014 02 0713 9


IP Logged 



towr
wu::riddles Moderator Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730


Re: HARD: Cigarettes Max Clique
« Reply #26 on: Jun 18^{th}, 2004, 12:25am » 
Quote Modify

Is there any proof in it that that's the definite answer? Cause I thought 'the' answer was unknown (unproven)..

« Last Edit: Jun 18^{th}, 2004, 12:35am by towr » 
IP Logged 
Wikipedia, Google, Mathworld, Integer sequence DB



Barukh
Uberpuzzler
Gender:
Posts: 2276


Re: HARD: Cigarettes Max Clique
« Reply #27 on: Jun 18^{th}, 2004, 3:53am » 
Quote Modify

on Jun 18^{th}, 2004, 12:25am, towr wrote:Is there any proof in it that that's the definite answer? Cause I thought 'the' answer was unknown (unproven).. 
 At least in the first edition of the book (some 30 years ago), it was not proven. Moreover, it was a kind of surprise for the author that 7 is possible.

« Last Edit: Jun 18^{th}, 2004, 4:19am by Barukh » 
IP Logged 



Jayaram
Guest


Re: HARD: Cigarettes Max Clique
« Reply #28 on: Aug 9^{th}, 2004, 4:27am » 
Quote Modify
Remove

Sorry for playing the fool  but isn't the question about infinite length cigarettes irrelevant? By definition, PARALLEL LINES ARE DEFINED AS LINES THAT MEET AT INFINITY. So, can't we just assume that infinite length cigarettes all meet at infinity (I know that the argument is ambiguous, but isn't that the very definition for parallel lines?


IP Logged 



Jack Huizenga
Guest


Re: HARD: Cigarettes Max Clique
« Reply #29 on: Aug 9^{th}, 2004, 9:43pm » 
Quote Modify
Remove

Parallel lines don't "by definition" meet at "infinity". It all depends on what type of geometry you are using. In standard Euclidean geometry, which is the geometry that nearly every "real life" question is worded in, parallel lines by definition never meet. Also, in Euclidean geometry there is no notion of infinity. I believe you are confusing projective geometry with Euclidean geometry. On another note, keep in mind that we are working in three dimensions. When working in three dimensions, one can't conclude that two arbitrary lines either intersect or are parallel like one can in two dimensions.


IP Logged 



