[seqfan] Re: Coins puzzle and a sequence

[Tanya Khovanova]

Yep,

Can you prove that for 7, 8, and 9 we need 3? (see my essay)

Tanya

--- On Thu, 7/2/09, Max Alekseyev <maxale at gmail.com> wrote:

> From: Max Alekseyev <maxale at gmail.com>
> Subject: Re: [seqfan] Coins puzzle and a sequence
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Cc: "Tanya Khovanova" <mathoflove-seqfan at yahoo.com>
> Date: Thursday, July 2, 2009, 11:10 PM
> On Thu, Jul 2, 2009 at 10:59 PM, Max
> Alekseyev<maxale at gmail.com>
> wrote:
> > On Thu, Jul 2, 2009 at 8:56 PM, Tanya
> > Khovanova<mathoflove-seqfan at yahoo.com>
> wrote:
> >
> >> You have 6 coins weighing 1, 2, 3, 4, 5 and 6
> grams that look the same, except for their labels. The
> number (1, 2, 3, 4, 5, 6) on the top of each coin should
> correspond to its weight. How can you determine whether all
> the numbers are correct, using the balance scale only
> twice?
> >>
> >> I haven't heard the correct solution from anyone
> yet.
> >
> > Are you sure that there is a solution?
> > I've performed the exhaustive search and found that
> for every pair of
> > scalings exposing perfect balance for correctly
> labeled coins, there
> > exists another (incorrect) labeling of coins that also
> exposes perfect
> > balance in both scalings.
> 
> Oh, I should have assumed that the balance scale does not
> only
> indicate imbalance but also what part is lighter/heavier.
> If so, there exists a number of pairs of scalings that
> solve the problem.
> 
> For example:
> 
> 6=1+2+3 and 1+6<3+5
> 
> 3+6>1+2+5 and 1+3<5
> 
> etc.
> 
> Regards,
> Max
>