Mistaken Identities: Scribal Errors or Conceptual Missteps in Ancient Chinese “Multiplication” Tables?

In 1913 the French Sinologist Émmanuel-Édouard Chavannes published a volume of material,mostly writings on wooden slips and boards, as well as some on paper, that Aurel Stein had acquired during hissecond expedition to China (1906–1908) and had entrusted to Chavannes for study, translation, andcommentary. Among these was a fragment of mathematics that Chavannes identified as a nine-ninesmultiplication table, which he duly transcribed, including what he took to be a mistaken total for all of themultiples listed as 1113. Although he was aware that the total of all the multiples he had transcribed came onlyto a total of 1111, he was at a loss to account for this discrepancy. Why should this nine-nines table end with a2“Total général” of 1113? It was not until three more nine-nines tables were discovered in 2002 at Liye in HunanProvince that further light would be shed on the situation of the nine-nines table for which Chavannes wastrying to find an explanation but could not.