correct winning play is not understood, a puzzle may well make a very good game.  Thus there is no doubt children will continue to play “Noughts and Crosses,” though I have shown (No. 109, “Canterbury Puzzles”) that between two players who both thoroughly understand the play, every game should be drawn.  Neither player could ever win except through the blundering of his opponent.  But I am writing from the point of view of the student of these things.

The examples that I give in this class are apparently games, but, since I show in every case how one player may win if he only play correctly, they are in reality puzzles.  Their interest, therefore, lies in attempting to discover the leading method of play.

392.—­THE PEBBLE GAME.

Here is an interesting little puzzle game that I used to play with an acquaintance on the beach at Slocomb-on-Sea.  Two players place an odd number of pebbles, we will say fifteen, between them.  Then each takes in turn one, two, or three pebbles (as he chooses), and the winner is the one who gets the odd number.  Thus, if you get seven and your opponent eight, you win.  If you get six and he gets nine, he wins.  Ought the first or second player to win, and how?  When you have settled the question with fifteen pebbles try again with, say, thirteen.

393.—­THE TWO ROOKS.

This is a puzzle game for two players.  Each player has a single rook.  The first player places his rook on any square of the board that he may choose to select, and then the second player does the same.  They now play in turn, the point of each play being to capture the opponent’s rook.  But in this game you cannot play through a line of attack without being captured.  That is to say, if in the diagram it is Black’s turn to play, he cannot move his rook to his king’s knight’s square, or to his king’s rook’s square, because he would enter the “line of fire” when passing his king’s bishop’s square.  For the same reason he cannot move to his queen’s rook’s seventh or eighth squares.  Now, the game can never end in a draw.  Sooner or later one of the rooks must fall, unless, of course, both players commit the absurdity of not trying to win.  The trick of winning is ridiculously simple when you know it.  Can you solve the puzzle?

[Illustration]

394.—­PUSS IN THE CORNER.

[Illustration]

This variation of the last puzzle is also played by two persons.  One puts a counter on No. 6, and the other puts one on No. 55, and they play alternately by removing the counter to any other number in a line.  If your opponent moves at any time on to one of the lines you occupy, or even crosses one of your lines, you immediately capture him and win.  We will take an illustrative game.

A moves from 55 to 52; B moves from 6 to 13; A advances to 23; B goes to 15; A retreats to 26; B retreats to 13; A advances to 21; B retreats to 2; A advances to 7; B goes to 3; A moves to 6; B must now go to 4; A establishes himself at 11, and B must be captured next move because he is compelled to cross a line on which A stands.  Play this over and you will understand the game directly.  Now, the puzzle part of the game is this:  Which player should win, and how many moves are necessary?