GG.30 Skip every 2 piece on the stones around a pond

Stones are arranged around the pond.
I walk around the pond clockwise by skipping every two pieces on the stones.

I start from a certain stone and when I stop on the stone at 2 round exactly, the number of stones stepped on while I was walking will become 18 in the stones around the pond.

Find the number of the stones arranged around the pond.

Answer all the probable numbers considered.

When exceeding the starting stone by the last one step, I shall stop with the starting stone without carrying out skipping every two pieces.

Answer

26 pieces
54 pieces