In October of 1779, Euler prepared for the St. Petersburg Academy a paper on “a curious question from the doctrine of combinations.” So great was the backlog of Euler's writings that this was not published in the Academy's Memoirs until 1811, more than a qurter-century after his death. This delay notwithstanding, he provided an example not only of a “curious” problem but also a method of attack—[redacted]—that has become one of the primary weapons in the combinatorial arsenal.
The problem had been posed, and solved, decades earlier. In 1708, Pierre Remond de Montmort (1678-1719) discussed a card game called Treizeor, more descriptively, Rencontre (“coincidence”). The rules are these: a player shuffles a deck of 13 cards from ace to king, then deals them one at a time saying “one” with the first card dealt, “two” with the second, and so on. Victory is achieved if at some point the card overturned exactly matches the word spoken—for instance, if the fourth card turned over is a “four” or the eleventh card laid down is a “jack.” should such a coincidence occur, the dealer wins.
Montmort determined the probability of winning thereby earning for himself a place of honor in the history of combinatorics....
—William Dunham, Euler: The Master of Us All
