On 3/25/07, Rajiv Mathews <[EMAIL PROTECTED]> wrote: > > > On 3/25/07, Prunthaban Kanthakumar <[EMAIL PROTECTED]> wrote: > > If you see carefully his proof does not assume anything about "sections > > colored continuously". His proof assumes only one thing "Half of them > are > > red and half of them are white" > > Half does not mean it should be continuous. So the proof still works > > correct unmodified even if the "halves" are not continuous. > > > > Could you elaborate please. > His proof contains, Quote: > "If r >= R-r, match half1 with Red half of outer disk. > Total matching = r + 100 - R + r = 100 - R + 2*r" > How do you justify this if the sections aren't contiguous? > I think the proof elaborated by _stone_ is correct and apt.
There is an "equivalence" It is simple.Just consider, Half1 = All the sections in the outer disc painted red (This is not continuous. But nothing prevents you from assuming a non-continuous 100 red sections as a logical half) Half2 = All the sections in the outer disc painted white Now with this interpretation, read his proof. Just remember that when you say 'half' of inner disc it means the sections corresponding to the half in the outer disc as defined above. This is the key to establish equivalence). Regards, Prunthaban -- > > > Regards, > Rajiv Mathews > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/algogeeks -~----------~----~----~----~------~----~------~--~---
