You can easily substitute the symbols for numbers, please do. I chose not to because I find it easier that way.

Now I've shown no long-term movement with 2 masses, you can expand the calculation for 20 masses. But why 20? Why not 10? 100? 2?


now when 1 reaches the end the most it can subtract is
25 kg.

This might be the crucial mistake.
If a mass has:
25kg and 1m/s. Momentum = 25kgm/s
Then it turns around in a u-bend, it ends up with
25kg and -1m/s. Momentum = -25kgm/s

The momentum has reduced by 50kgm/s!!!! Not 25.


I never said the ends were brakes their just turnarounds.

Yep. If an object just turns around, then its moment becomes the negative of what it was before. Bounce a ball against a wall, and it's direction changes to negative, but its speed remains roughly the same. It's lost TWICE the momentum it had.