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Nigel_Parsons
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 Re: HARD: Cigarettes Max Clique   « Reply #25 on: Jun 17th, 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
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towr
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 Re: HARD: Cigarettes Max Clique   « Reply #26 on: Jun 18th, 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 18th, 2004, 12:35am by towr » IP Logged

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

on Jun 18th, 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 18th, 2004, 4:19am by Barukh » IP Logged
Jayaram
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 Re: HARD: Cigarettes Max Clique   « Reply #28 on: Aug 9th, 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?
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Jack Huizenga
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 Re: HARD: Cigarettes Max Clique   « Reply #29 on: Aug 9th, 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.
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