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Amusements in Mathematics

Moving Counter Problems
"I cannot do't without counters."
Winter's Tale, iv. 3.
Puzzles of this class, except so far as they occur in connection with actual games, such as
chess, seem to be a comparatively modern introduction. Mathematicians in recent times,
notably Vandermonde and Reiss, have devoted some attention to them, but they do not
appear to have been considered by the old writers. So far as games with counters are
concerned, perhaps the most ancient and widely known in old times is "Nine Men's
Morris" (known also, as I shall show, under a great many other names), unless the
simpler game, distinctly mentioned in the works of Ovid (No. 110, "Ovid's Game," in The
Canterbury Puzzles), from which "Noughts and Crosses" seems to be derived, is still
more ancient.
In France the game is called Marelle, in Poland Siegen Wulf Myll (She-goat Wolf Mill,
or Fight), in Germany and Austria it is called Muhle (the Mill), in Iceland it goes by the
name of Mylla, while the Bogas (or native bargees) of South America are said to play it,
and on the Amazon it is called Trique, and held to be of Indian origin. In our own country
it has different names in different districts, such as Meg Merrylegs, Peg Meryll, Nine Peg
o'Merryal, Nine-Pin Miracle, Merry Peg, and Merry Hole. Shakespeare refers to it in
"Midsummer Night's Dream" (Act ii., scene 1):—
"The nine-men's morris is filled up with mud;
And the quaint mazes in the wanton green,
For lack of tread, are undistinguishable."
It was played by the shepherds with stones in holes cut in the turf. John Clare, the peasant
poet of Northamptonshire, in "The Shepherd Boy" (1835) says:—"Oft we track his
haunts .... By nine-peg-morris nicked upon the green." It is also mentioned by Drayton in
his "Polyolbion."
It was found on an old Roman tile discovered during the excavations at Silchester, and
cut upon the steps of the Acropolis at Athens. When visiting the Christiania Museum a
few years ago I was shown the great Viking ship that was discovered at Gokstad in 1880.
On the oak planks forming the deck of the vessel were found boles and lines marking out
the game, the holes being made to receive pegs. While inspecting the ancient oak
furniture in the Rijks Museum at Amsterdam I became interested in an old catechumen's
settle, and was surprised to find the game diagram cut in the centre of the seat—quite
conveniently for surreptitious play. It has been discovered cut in the choir stalls of several
of our English cathedrals. In the early eighties it was found scratched upon a stone built
into a wall (probably about the date 1200), during the restoration of Hargrave church in
Northamptonshire. This stone is now in the Northampton Museum. A similar stone has
since been found at Sempringham, Lincolnshire. It is to be seen on an ancient tombstone
in the Isle of Man, and painted on old Dutch tiles. And in 1901 a stone was dug out of a
gravel pit near Oswestry bearing an undoubted diagram of the game.