491

WHITE.

1. K. to Kt.'s 2nd.

Diagram 120.

BLACK.

And the situation is the same as at the 2nd move of Diagram 118.

We have already observed that in similar positions, but one step further advanced, the King, if he have to move, would lose. The student having examined the above will find the solution easy. We only, therefore, give four more examples, where in all cases the Pawns win.

Diagram 122. If the Pawns move, they play P. to K. B's 6th, or, if K. moves, and is played to Kt.'s 2nd, they advance R. P., if to R's 2nd, they move B. P.

Diagram 123. The Pawns having to play, move P. to B's 4th; on the contrary, had the King the first move, this Pawn would play to B's 3rd only, thereby gaining a move.

Diagram 124. Here also the unmoved Pawn advances one or two squares, accordingly as the King has or has not the first move. If the Paw move first,

The

Diagram 125. The position is similar to the two preceding ones. Pawns winning by their power of playing the unmoved Pawn one or two squares at pleasure. For example,

3

3

Had the King here originally stood at B's 3rd, or R's 3rd, the party moving first would have won.

It would obviously be easy to multiply these examples to an indefinite extent; the foregoing, however, will be sufficient to exemplify the principle with which we set out, viz., that the King can always stop the Pawns when he is originally upon any square in front of them, or when he can reach his Kt.'s 3rd sq. within three moves. It will also be clear (from the three last positions) that whenever two of the Pawns can succeed in advancing unattacked to their fifth squares, with the third unmoved, they invariably win, wherever the adverse King may be.

Suppose, then, that the White King originally stood on his Queen's square, (the Pawas being unmoved,) it follows that whoever has the move must win; because, if the King move he has time to place himself on the Kt.'s 3rd sq. within three moves, but if the Pawns move they will be able to prevent his doing so; thus:

(If the King retreat, Black will play P. to B's 5th, &c.)

4. P. to Kt.'s 4th (ch.)

&c., &c.

The Pawns win as in a former example.

foregoing examples naturally lead us to the consideration of the re cox positions arising from King with Rook's, Knight's op's unmoved, against a similar opposing force.

KING AND THREE PASSED PAWNS AGAINST KING
AND THREE PASSED PAWNS.

With the Pawns placed as in the Diagram above, the two King may occupy a great variety of situations on the board, producing, of course, different results, according as they may relatively be more or less advantageously situated. However varied the position of the two Kings, either player may, nevertheless, readily discover whether his position be a winning or a losing one, by observing the following rules.

To simplify the matter, all the possible positions that may be assumed for the two Kings are divided and classed under the two following cases:Case 1. When both the Kings are more than three moves distant from their respective master squares.

Case 2. When one or both Kings are within three moves of their master

squares.

With respect to the first case, it has already been shown that, under the conditions named, the King cannot prevent the adverse Pawns from going to Queen. Each party will, therefore, make a Queen, and the game ought to be drawn, unless one of the Kings happen to occupy a square in the royal rank, in which case he would lose, as the adversary would Queen a Pawn, checking, &c. None of the positions falling under the first case produce any interesting situations, nor afford much scope for play.

The game, however, becomes totally altered in its character in all the numerous situations included in Case 2, wherein the party should win whose King is most advanced in the game, and to ascertain which of the two Kings is so in advance, observe the following General Rule.* "Victory

*An exception to this Rule is, when one of the Kings stands so near the adversary's Pawns as to prevent them being moved two squares without being captured.

will be in the hands of the party who can first play his King into its mas. ter square." The power of arriving first to this square will result either from the advantage of the first move, or from being originally placed nearer to it.

The proper mode of play is the following:-The player having the win. ning position (which suppose to be the White), should have in view to advance his Pawns until they are stopt by the Black King. White will then stop the Black Pawns, which will compel the Black King to move out of position, and the White Pawns will afterwards go forcedly to Queen. (This will be shown in the 1st Example.)

In cases where the Black (when losing player) would force his Pawns to be stopt first, the White would still win, for the Black would not afterwards be able to stop the White Pawns. This is shown in the 1st Variation to the 1st Example.

In conducting his game the player having the winning position must be cautious of two things, and which, it is probable, were the chief difficulties that had so long retarded the solution of the "Three Pawn Problem." 1st. Before advancing his Pawns he must take care that his King be near enough to the adverse Pawns to prevent two of them reaching their fifth squares with the third Pawn unmoved. Were this permitted, the game would be drawn, as shown in the 1st Variation to the 2nd Example. When, therefore, his King is three moves distant from the master square, he must begin by moving his King, and not his Pawns, as the 2nd Example and its 1st Variation will prove.

2nd. The winning player must be careful when advancing his King to oppose the adverse Pawns, to stop them in the fewest possible number of moves, for the loss of a move would be the loss of the game. As an error of this kind may be easily committed, two examples are given as illustrations. (See 2nd and 3rd Variations to 1st Example.)

FIRST EXAMPLE.

GRECO'S POSITION. Diagram 127.

BLACK.