To try to come up with a design for the mechanical counter competition, I came across the classic mechanical counter design used in automobile odometers and gas meters before electronics took over the market.
You might want to incorporate this design approach into your design for a mechanical counter.
The smallest gear has 8 teeth on the top and four teeth on the bottom. The four teeth on the bottom rest against the underside of the right disc and prevents any movement of the left disk when the right disc is turning.
The right disc has a couple of teeth that engage the small gear once each revolution.
Each time the right disc is turned a full revolution, the left disc turns 36° or 1/10 of a revolution. If there are 10 numbers added to the left disc, it advances one digit.
When turning the right disk quickly, the tooth advance on the left gear is almost invisible. This turns the project into a fidget??
The author marked this model as their own original creation.