It can be argued that the beads in this first column could have been used as originally believed and widely stated, i.e. as ½, ¼ and ⅓ and ⅔, completely independently of each other. However this is more difficult to support in the case where this first column is a single slot with the three inscribed symbols. To complete the known possibilities, in one example found by this author, the first and second columns were transposed. It would not be unremarkable if the makers of these instruments produced output with minor differences, since the vast number of variations in modern calculators provide a compelling example.