> You drew some lines in the sand, some rows and columns. The rows represented the digit magnitude (I, V, X, etc). The columns were for the operands. Two column

> You drew some lines in the sand, some rows and columns. The rows represented the digit magnitude (I, V, X, etc). The columns were for the operands. Two columns for a number. Why two? Because Roman numerals sometimes use negative digits. Note that this is speculative. We don’t actually have descriptions of how Romans set up or used their counting boards, only indirect evidence that they did most arithmetic and accounting with them. The digits probably went left to right or right to left rather than top to bottom (there is some written account of IIRC Greek and Egyptian counting boards going opposite directions). The more specific and complete evidence we have today is from medieval Europe, where typically digits were rows and tokens on the lines were used for 1, 10, 100, etc. with tokens in spaces between the lines used for 5, 50, 500. However, since counting board arithmetic was a skill taught directly as oral tradition, most practical algorithms (especially those used by specialists for more obscure operations) have been lost. We can do some additional speculation based on methods used today on bead-on-rod sorobans/suanpans from Japan/Korea/China. We can speculate (from occasional examples in writing of IX to represent VIIII, etc.) that Romans may have (sometimes? often?) represented "negative" counts on the other side of a dividing line, but this does not have direct evidentiary support. * * * For more elaborate speculation about setup and algorithms, Steve Stephenson has done quite a bit of thinking about practical uses of counting boards. It’s impossible to judge how close this is to what ancient people actually did, but it’s interesting in itself, and IMO worth teaching to young children today as a complement to pen and paper (and mental) arithmetic. I think it is a better intellectual tool than the sliding-bead soroban. My kids use some nice metal buttons as counters: https://ethw.org/Ancient_Computers https://ethw.org/Ancient_Computers