#### Hint for Check Point :

Turn $2$ - $8$ - $17$ into $4$ - $7$ - $16$

then $4$ - $7$ - $16$ into $3$ - $9$ - $15$

#### Hint for proving the odd one is impossible :

This example isn't the same thing but might give you a clue
about the kind of thinking to try.

In a $4$ circle problem and using $26$ stones the distribution
$1$ - $4$ - $7$ - $14$ cannot be turned into $3$ - $5$ - $7$ -
$11$

To understand why notice that in the first there are two odd and
two even numbers while in the second the numbers are all odd.

On a "move" one value goes up by $3$ and the others go down be
one.

What will happen to odd and to even numbers?

The Odd Stones problem isn't about odd or even numbers but a
similar kind of thinking could be useful.

Good luck!