I used the same way, a blank sheet of paper and a pencil to develop my routine.

Then I placed AND, OR, NOT, EXOR and connections on it with the limitation of only 2 inputs for every gate.

Then I optimized it for a minimum count of wires (= register) and logic gates or connections (= instructions).

I think this is the typical way for erstwhile hardware logic developers.

That this solution was named "vertical counters" I have only seen recently.


Peter