I did assume that the outer disk is painted half (contiguous) red and half
white.
However the 'equivalence' should do the trick and the same proof applies.
As far as Stone's proof goes, I did not understand -
For each inner section,no matter white or black ,there is 100
color-matching events.
Can somebody explain?
~Vishal
On 3/25/07, Prunthaban Kanthakumar <[EMAIL PROTECTED]> wrote:
>
> Ouch.... I got the question completely wrong assuming the inner disc is
> continuous.Sorry for the confusion.
>
> On 3/25/07, Prunthaban Kanthakumar < [EMAIL PROTECTED]> wrote:
> >
> > 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
> > >
> > >
> >
> > > >
> >
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