The most rudimentary (prior to computers) number system is the Unary number system, consisting purely of 1s or strokes, usually representing tallies. It is described as a base 1 number system.
I studied it in my Computer Science classes (way back when) in a course about Computability, Turing Machines and Automata Theory. In particular, the Turing Machine example described a machine readable tape containing groups of 1s each separated by a single 0.
I used it as a child/teenager to count up physical items in several categories (popularity counts) and for keeping score in pool. Remember that this was *before* computers existed. Also, not all pool halls had an overhead Abacus. I was much more intimate with the physical world then.
The problem, as I see it, in this variant of Sudoku is that there’s absolutely no space to insert candidate (little) numbers based on which logic is performed. One possibly impractical solution is to do this on a classroom size whiteboard. But I warn you: Don’t have a stroke!