shed by me in
_Tit-Bits_ some years ago.

On an open level tract of country a party of Russian infantry, no two of
whom were stationed at the same spot, were suddenly surprised by
thirty-two Turks, who opened fire on the Russians from all directions.
Each of the Turks simultaneously fired a bullet, and each bullet passed
immediately over the heads of three Russian soldiers. As each of these
bullets when fired killed a different man, the puzzle is to discover
what is the smallest possible number of soldiers of which the Russian
party could have consisted and what were the casualties on each side.

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 dis