Black takes the man on square 11, which gives him a leading place on the board.

Instead of playing 25 to 22, many think that 28 to 24 is a better move. This, however, is open to question. Let us proceed with the game from the above point.

The last move of White gives him a certain advantage, but he must be careful not to move the man from square 24 to square 19, or Black by giving the man on 10 will win two for one. Black proceeds:—

If White had moved 27 to 23, he would have lost a man, for Black would have taken the piece on 24, and obliged his opponent to go from 31 to 24; and then, by moving into square 20, compelled White to go from 24 to 19, and have gained the exchange by giving the man on 10. Therefore 30 to 25 is the best.

Black has now the choice of two moves. Apparently he must lose a man, but by moving 16 to 19 he forces an exchange, which leaves him either even or a man ahead, according to White’s play. He moves from 16 to 19, and White may either take the man on 11 or the two men on 19 and 11.

And the game assumes the following position:—

Which is to win? It is Black’s move.

THE WHILTER OPENING.

This, like many others, is a modification of that best of all openings, the Old Fourteenth; the moves are—

This is the opening. It may proceed in many ways. The better, perhaps the best, plan is thus:—

Had Black moved 16 to 20, he would have lost a piece by his opponent playing 29 to 25—

which leaves the position thus:—

Black now usually plays from 1 to 5, and has a good sound strong game.

CHAPTER XIV.—SOLITAIRE.
By the late Captain Crawley.

As a game for one player there is no superior to Solitaire. Apparently easy and simple, it is really intricate and scientific. Governed by a well-defined principle, chance forms no element of its practice. Like Chess and Draughts, it is entirely a mental and demonstrable game, full of variety, and affording ample scope, in its almost endless combinations, for the display of thought and ingenuity.

Solitaire is played on a board of thirty-three holes, in each of which a marble or glass ball is placed. Solitaire boards are made, but the game may be just as efficiently played on a properly marked piece of card-board, with draughtsmen or counters instead of marbles. This plan, indeed, is preferable to and cheaper than any other.

The method of play is as follows:—One marble is removed from its place, and then another is passed into the vacant hole. Take up the marble over which you jump, and continue to take piece after piece, always going in straight lines and never in diagonals, till you bring back the last marble from the hole whence the first was taken. One marble only can be taken at one jump; but, as in Draughts, you may proceed to play, and take, with the same marble, so long as there is a piece en prise with a vacant hole in the line behind it. The repetition of the figures will show the continued move of the piece.

There are other modes of playing Solitaire—as by indicating a special hole, distinct from the starting-place, in which to lodge the last marble, leaving two, three, or four marbles in a particular position, ending in the hole next the original one, and so on; but the above, the more usual plan, should be first learned. We will now give a diagram, and show you how to start from and return to the centre hole. Remove the centre marble. Jump from 1 in the upper limb to 1, the middle hole, taking 16-18. Go from 2 on the right limb of the diagram to 2 above the centre, taking 3-5. Proceed from hole to hole as indicated by the figures, and you will find that the last move will land the marble in the centre. Practise this till you can play the Centre-hole Game without the use of the diagram. It looks easy enough; but just try it before you condemn Solitaire as mere child’s play.

GAME II.

Presuming you have familiarised yourselves with the principle of the game, I present another diagram:—

Remove the marble from the upper right-hand corner hole and proceed as before, going from place to place, as shown by the figures on the diagram. Get this by heart, and play the game without the problem.

GAME III.

In this, one of the best positions, remove the left-hand upper marble, and play the game according to the plan in the diagram below. You will find this an easy game to remember.

This may be altered by ending in any other hole. You should, however, thoroughly conquer the game as presented before you attempt any variation. It is not sufficient to play with the diagram before you. The problem is presented as a game to be learned, and once thoroughly learned, it is difficult to forget it.

GAME IV.

The following is a pretty but somewhat difficult position. It will be sufficient to give the diagram without remark other than this: Conquer it before you leave off, and do not be disheartened if you fail to succeed the first time you attempt it without the diagram.

GAME V.

You will understand that these positions given may be varied by starting from a similar place in either leg of the board. It is sufficient to mention this. To give players many variations would occupy too much space.

GAME VI.

Here we have one of the most difficult and yet most interesting of positions. Proceed as before, taking care to learn the game so as to play without the numbered diagram. Remove the black marble.

Solitaire may also be played by two persons, the object of one of them being to defeat the other by contrary or opposite moves. Double Solitaire is, however, somewhat deficient in the one great element of all antagonistic games—variety.

CHAPTER XV.—FOX AND GEESE.
By the late Captain Crawley.

I am not sure that this game was not played by the boys of ancient Greece and Rome; or perhaps even by boys in a yet earlier age of the world. At any rate, it is a very, very old game, of whose origin nothing whatever is known. Under these circumstances, it would be easy to gossip on for a page or two, and talk about anything likely to seem interesting; but it is pleasanter, and much more practical, to tell you how, with the assistance of our Solitaire-board, and some draughtsmen or counters of wood, bone, or metal, you may play it yourselves.

For Fox and Geese you need seventeen counters of one colour, to represent the Geese, and one counter of a different colour for the Fox. You prepare the board thus: place the Fox in the middle and the Geese in front, as in the diagram below.

Like Chess and Draughts, it is purely a game of strategy for two players. The usual plan is for each player to take the initiative in turn, the Fox in one game and the Geese in another. Unlike card games, it contains no element of chance or ‘luck.’

The whole motive of the game is for the Fox to catch the Geese, or for the Geese to drive the Fox into a corner from which he cannot escape. Properly played, the Geese, with the first move, must always win; but in this game, as in real life, the more cunning creature is not seldom successful.

The plan of the game is this. The Geese march forward only in straight lines, down or across; the Fox can move forward, backward, or sideways on the straight lines, not the diagonals. The Fox takes any Goose that may be en prise with a vacant space behind, as in Draughts; and so long as he can take, he continues his move. When he succeeds in following up and catching all the Geese, one after another, he wins. But the Geese, if they only go boldly to work, can drive him away. They must go forward as a phalanx with determination, filling each vacant spot, and leaving no loophole into which the enemy can jump or creep. All depends on united and determined action. United they conquer; separated they fall. When their number is reduced to six, it is impossible for them to confine the Fox. But there is no reason why it should be so reduced. Look at the diagram. If we call the upper left-hand spot 1, and number the board horizontally to 33, at the lower right-hand corner, we shall soon see how the attack may be conducted. The Fox is in the centre; the Goose on either of the central junction lines can move without fear of capture, and the Fox must retreat. Having, say, moved 11 to 18, the Goose on 6 moves on to 11. The Fox is still without power to harm. The Geese proceed to go forward, and in this way ultimately force their enemy into a corner, or they may beguile him by offering a bait. Say the Goose on 15 moves to 16, the Fox must take him and lose his central position of attack. The Geese follow up their advantage; and, unless they commit some grievous error, they pin Master Reynard in a corner, whence he can by no means get out. The whole principle of the game is Advance. Go forward with the stronger force; fill up all vacancies. Directly a Goose moves on, back him up. Surround your enemy and compel him to retreat. As to the Fox, his tactics must be bold, yet cautious; determined, yet crafty; daring, yet subtle; adventurous, yet shrewd! Very like real life, is it not?

The game can be varied by placing the Fox on another spot; or by insisting on his catching all the Geese; by the latter taking the horizontal limits of the board only, or by offering odds, and so on; but the plan here given will be found ample in providing rational amusement for winter evenings. Less scientific, certainly, than Chess or Draughts, it affords abundant opportunities for thought and mental calculation.

CHAPTER XVI.—GO-BAN.
By Herr Meyer.

This game is of Japanese origin, and the name means Go = five, and Ban = board. It has, however, become gradually corrupted into ‘Go-bang,’ and thus it is now generally written.

In Japan it is played on a board of more than three hundred squares, but in Europe on boards of sixty-four squares (as in chess and draughts), or on larger boards. The Japanese have schools for the study and practice of the game, and divide the players into nine classes. A late account says that at present there is no player of the highest (the ninth) class living; but one of the eighth class, named Murase (in German spelling pronounced Moo-răh-sey), is editing a periodical, in which he publishes the theory of the openings, actual games, problems, poems, &c.

This game of Go (or game of five) is in China called Ki (= Kee), and was invented there about 2,000 years B.C. It is therefore older than chess. It was introduced into Japan about 1,100 years ago, and was there brought to higher perfection.

It is played by two persons. In Japan they use more than a hundred men on each side. If played on the chess-board, then generally one plays with twelve white men, the other with twelve black men. The aim of each player is to get five men in a line—i.e., five of his men close together in a straight line, either in row, a file, or a diagonal. In Japan each player tries to form a chain with his men around the others, etc.

The play is carried on thus:—The players decide as to first move; afterwards they begin alternately. The first player, say White, places a man on any of the sixty-four squares, then Black places a man on any of the remaining sixty-three squares: thereupon White puts down his second man on any unoccupied square, and so on until all the twenty-four men are placed. Now the moving begins. The first player moves one of his men to any of the next unoccupied squares, but must not leap over a man, and the second player proceeds in the same manner. So the play continues until one or the other succeeds in getting five men in a line.

Thus the play consists in placing and moving. If a player be not sufficiently attentive he can lose in the first part of the game. The moving may extend from two or three to any number, according to capacity of the players.

The game requires a great deal of watching, for the ‘Go,’ or ‘Five,’ can be made in any of four directions—horizontally, vertically, or on the right and left diagonals. There are eight lines for each of the two straight ways, and seven lines for each of the two diagonal ways; in all thirty lines. Four positions of the ‘five’ are possible in a row or a file, and as many in each of the longest diagonals, whilst the shortest diagonal permits of only one position, so that the number of all positions is 4 × 8 + 4 × 8 + 2 (4 + 3 + 3 + 2 + 2 + 1 + 1) = 96.

Many players prefer this game to draughts. It may also be played by four persons, taking partners as in ‘whist,’ when each player receives six men. Odds can be given in this game, a superior player having eleven against twelve men.

Whenever a player has three men in an open line the opponent must stop him, for should he get four, then the adversary could block him on only one end. This blocking, however, is not necessary if the second player can first make ‘five.’

The student will learn the method of playing from the games we shall give with explanations. The system of description is the International Chess Notation, as will be shown on the frame of the diagram to follow. The letters in brackets after the moves will refer to the explanatory notes.

The following two games were played between G. W. S. and H. F. L. M.:—

The men are now placed as shown in this diagram:—

Now the moving begins:—

Notes.

(i) Experience has shown that it is best to occupy the central squares, for the men then have the greatest freedom of action.

(j) This move is necessary, for if Black had placed the man on c5, White would have won by placing his next man on c4 or g4.

(k) He must block the line at a2 g8, just as well as Black must now block the f file.

(l) The last six moves were all forced for Black.

(m) A weak move, which places the black men awkwardly. He would have done better to place it on b3 in order to force the last white man to go to a2, and then Black could have placed his last on c3, and try to make a ‘five’ in the a5 e1 or the a6 f1 or the c file.

(n) Necessary, for if placed on b6 or a5, White would have won thus:—g6 g7, f6 g6, g5 f6, followed by g7 f8.

(o) Endeavouring to bring this man to the other side of the board.

(p) He is afraid of e1 e2.

(q) A bad move, for although he can block at h6, he can afterwards not stop the g or f file. Black should have tried to move from c6 to a2.

(r) Must. White now wins easily, even if e6 stood on e7, for g6 g7, e7 f8, f7 g8, f6 g6, f4 e5, g6 f6 (else f5 f6), f5 g6.

Game No. 2.

Between H. F. L. M. (White) and G. W. S. (Black).

The position is now so interesting that we give it on a diagram.

It appears at first sight that White might now place his last man on h8 and win. Black would then be obliged to place his last man on f6. White would continue f5 g4, and Black must answer h7 g8, and White would now win with e5 f5, followed by h8 h7, if Black could not play e7 f7 and come first in making ‘five’ in the diagonal a2 g8. To prevent these ‘five’ of Black, White would have to play g7 f7 (instead of e5 f5), and then Black would win easily by c3 b2, followed by e3 f2. White therefore must place his last man so that he can at once stop the approaching line of ‘five’ in the second row. He might place it on f2, but does better to put it on g3, and thus compel the last black man to go to g4. Therefore the game went on thus:

All the men are now well placed, and the moving can begin.

Notes.

(i) These two moves of Black were compulsory.

(j) Must, because he cannot stop the line at d1.

(k) White now threatens to win by c5 c6 and on to c7.

(l) A good move to go on to h2.

(m) He ought to have played c6 d7, then the game might have proceeded thus: e8 d8, d7 c7; e4 d5, e7 d7; d6 c6, c4 b5; d3 c4, h4 g4; c5 b4, any; e5 e4 = five.

(n) There are now two lines for White, and only one can be stopped.

The third game between these two players had twenty-four moves, lasted about half an hour, and was won by the second player (M.). The fourth game lasted two hours, had seventy-five moves, and was won by the second player (S.).

Game No. 3.

Played between H. M. (White), and L. S. (Black).

White to play, and win in five moves.

The white men are on the squares b4, c2, c4, c5, c6, c7, d4, e3, e4, e5, f2, and g4.

Notes.

(a) He must prevent the man going from f3 over g2 to g1.—If he were to play g3—g4, White would answer e4—f5, and win in two more moves by making a ‘five’ in the diagonal a7 g1.

(b) Any other move would not prevent White from making ‘five’ in the second row, for Black must not move the man c3, as White would obtain ‘five’ (or even six) in the c file.

CHAPTER XVII.—THE MALAGASY GAME OF FANÒRONA.
By W. Montgomery.

Nobody can very long reside in Madagascar, or in the central parts of it at any rate, without occasionally observing little companies of the natives bending eagerly over some mathematical-looking diagram rudely scratched on a roadside stone, or on the top of a rock, or, more roughly still, on the sun-baked clay of the wayside. If you look a little at the figure of the diagram, and consider the multiplicity of squares, diagonals, and adjacent parallelograms involved in it, you may think the people are discussing some Malagasy rider to one or other of the propositions in the Second Book of Euclid. Take the trouble to ask, however, and you will find that they are simply playing at their national game, the Fanòrona.

The fanòrona board is a rectangular parallelogram, divided into thirty-two equal spaces. Gather these, in your eye, into eight larger squares, containing four each; draw the diagonal lines in each of the eight, and the fanòrona figure is complete. Forty-four movable pieces are required for the game—twenty-two on each side.

With the Malagasy these are usually little pebbles and potsherds, or beans and berries. We, however, will call them the Black and the White pieces. The two players sit opposite each other, having the long sides of the fanòrona adjacent to them. The pieces are then arranged on the corners or angle-points; not on the squares, as in chess or draughts. There are five of these long lines on the board, each containing, of course, nine angle-points, and the pieces are thus arranged:

The third, or central line, is occupied by the eight remaining pieces, placed alternately, thus:

One point remains unoccupied, the central angle-point of the board, the fifth of the third line. This represents the royal seat in the public gatherings, but in the fanòrona game it is called the foibeny (‘navel’).

The object aimed at by each of the players is, as in draughts, to remove the whole of the adversary’s pieces from the board. But much caution is required, for we shall see that a few pieces well posted may easily annihilate more than four times their number in weaker situations; and, as in real warfare, even the very numbers of a force may sometimes prove their ruin. A few examples here will show the various ways in which the game may be opened, the manner in which the pieces are moved, and the adverse pieces captured. Let us suppose that the pieces are all placed, as just described above (see diagram 1). For convenience of description let the five lines on which the pieces are posted be called respectively A, B, C, D, E, instead of first line, second line, third line, etc. Any one of these letters, then, with a numeral appended, will be an easy reference to the piece that is to be moved, or to the vacant point to which a piece has to be removed, or to a hostile piece that has to be captured and removed from the board (see diagram 2). Then remember:

Firstly, that a piece may be moved in any direction,—forward, backwards, sideways, or diagonally to the first station in that direction, if such station be vacant.

Secondly, if there be now no other vacant station between the attacking piece just moved and the enemy’s pieces along that line, these, whatever their number, are captured at once, as far as they stand in unbroken order on the line attacked. If, however, a vacant position occurs in their line, or another hostile piece is among them, then only the piece or pieces nearest the assailant are captured.

Thirdly, the pieces of the enemy may be captured by a retreat as well as by an advance. A piece that has been standing in a station adjoining to some piece or pieces of the enemy may capture it or them by retreating one point along that line, if such point happen to be vacant. The limitation defined immediately above applies in this case also.

Fourthly, at the beginning of a game one move only is permitted to the first side. After that side has moved once, any piece that is moved is permitted to run amuck in the enemy’s lines, and go on as long as he finds foes to capture, provided (a) that he does not return immediately to any point he has just left, and (b) he cannot take a foe behind him immediately after taking one in front of him, nor one on his right hand immediately after taking on his left hand, and vice versâ. ‘Don’t eat at both ends, like a leech,’ says the Malagasy proverb.

Let us suppose that White is going to move first at the commencement of a game. There is only one vacant point on the board into which he can move a piece, namely, the foibeny or central point, which we may term C5, as it is the fifth point of the third line. There are four white pieces, any one of which may be moved into the vacant post, those on C4, D4, D5, D6. If he advances D5 to C5, then he immediately captures Black’s pieces on B5 and A5. Black may now retaliate by withdrawing his piece on B6 to A5, thereby capturing White’s pieces on C7, D8, E9. White may now, in any one of several ways, inflict a series of severe strokes on the unfortunate Black. Thus, for example:

Now the White piece must stop awhile, for although the Black piece at B7 is under his range, yet in taking it he would be transgressing the two laws mentioned above. He would have to return to B6, which he has just quitted, and he would be ‘eating at both ends like a leech,’ which is improper. But the Black piece on B7 may now very properly provide for his own safety and circumvent his assailant by advancing thus:

These moves are not given as examples of what the Malagasy would consider good play, but simply to show the modus operandi of the game.

If the game happens to terminate in a ‘draw,’ which is frequently the case, then the combat may be recommenced on the same terms, the other side now taking the first move. Should one of the players have been defeated, however, he is not allowed to play on the same footing as before, for the game must be altered in a kind of mocking condescension to his weakness. The new form of the game is called véla; the one who has conquered is the mpàmpihinam-béla (he who allows to graze at large). The defeated is hómam-béla (a poor sheep not to be molested for awhile in his pasture-ground). The véla game is opened by the vanquished, and the victor exposes such of his pieces as he chooses to surrender to his antagonist. These pieces may only be taken singly, and the generous conqueror refrains from taking any of his enemy’s pieces until he has parted with, one by one, seventeen of his own; then with the remaining five he begins his campaign against the undiminished forces of his antagonist. If he be a skilful player, however, he has managed meanwhile to occupy the fortress positions of the game, and the hosts of the enemy are probably huddled together in such situations that he will come down on them ‘like a wolf on the fold.’ If the hómam-béla is again defeated he is only allowed to play the véla form of the game until he has redeemed himself by a victory. Or he may choose to humiliate himself by openly confessing his inferiority, though, as one of my informants says, ‘few of the Malagasy are willing to do that.’ In ancient times grace was accorded to the beaten combatant on condition of his kneeling down before his conqueror and bleating like a sheep (mibàrarèoka), in confession of his weakness.

Here is a specimen of the véla game, including the preliminary sacrificial moves by which Black gives up, one by one, the fated seventeen pieces. Then the time of reprisals comes, and the five survivors take the field, and give and take no quarter.

CHAPTER XVIII.—THE AMERICAN PUZZLES.

These puzzles, known as the ‘Thirty-four Game’ and the ‘Fifteen Game,’ on their introduction amongst us some years ago, created general interest wherever tried. Both games are played on the same board. The ‘blocks’ may be readily made by any lad. They can be cut out of cork, wood, or other suitable material, and may be square or round in shape, the numerals being written on the upper side, thus—