If he has a plantation of forty-nine trees, planted in the form of a square as shown in the accompanying illustration, he wishes to know how he may cut down twenty-seven of the trees so that the twenty-two left standing shall form as many rows as possible with four trees in every row.

Of course there may not be more than four trees in any row.

213.—­TURKS AND RUSSIANS.

This puzzle is on the lines of the Afridi problem published 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.”