# [seqfan] Re: Coins puzzle and a sequence

Max Alekseyev maxale at gmail.com
Fri Jul 3 04:59:46 CEST 2009

```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.
In other words, if the coins are labeled correctly, that cannot be
surely established using just two scalings.

For example, while scalings 1+2+3=6 and 2+4=6 give perfect balance for
the correct labeling of coins, they also give perfect balance for the
labeling where labels 1 and 3 are swapped.

Regards,
Max

```