Here's a device I made with a laser cutting machine. It is intended to count points for any game. Those models have two cylinders but the principle is the same to make a three cylinders counter.
Step 1: Pieces After Cutting
Here are the pieces. To ensure that each number will stay in place and move from one position to an another with a click, I used 3mm cube magnets. I used 3mm plywood for the construction.
Step 2: Inserting the Magnets
By reducing the size of the hole it must be possible to place the magnets without glue. The right dimension depends on the material and laser cutting machines.
Magnets have to be placed in the same direction. Each disc has to fix itself to the other
Step 3: Fixing the Axle
The axle is a pair of forks. They can be glued, or two magnets can also be used to secure each fork together. The magnets on the disks are so strong that the axle is almost superfluous. At this stage, if glue is used, it is important to be sure, it won't fix the discs together.
The last step consists in the construction of the cylinder. Be careful to respect the number order and facing.
The project has been made in the Lorem fablab in Paris (lorem.org)
The source file is an inkscape SVG file.
This project is free: Free art licence or CC by sa 4.0