#### $27$ stones are distributed between $3$ circles

On a "move" a stone is removed from two of the circles and placed
in the third circle.

So, in the illustration, if a stone is removed from the $4$ and
the $10$ circles and added to the $13$ circle, the new distribution
would be $3$ - $9$ - $15$

#### Check you can turn $2$ - $8$ - $17$ into $3$ - $9$ - $15$ in
two "moves"

Here are five of the ways that $27$ stones could be distributed
between the three circles :

$6$ - $9$ - $12$

$3$ - $9$ - $15$

$4$ - $10$ - $13$

$4$ - $9$ - $14$

$2$ - $8$ - $17$

There is always some sequence of "moves" that will turn each
distribution into any of the others - apart from one.

Identify the distribution that does not belong with the other
four.

Can you be certain that this is actually impossible rather than
just hard and so far unsuccessful?