[seqfan] Re: Coins puzzle and a sequence

[Max Alekseyev]

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