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353.—­THIRTY-SIX MATES.

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Place the remaining eight White pieces in such a position that White shall have the choice of thirty-six different mates on the move.  Every move that checkmates and leaves a different position is a different mate.  The pieces already placed must not be moved.

354.—­AN AMAZING DILEMMA.

In a game of chess between Mr. Black and Mr. White, Black was in difficulties, and as usual was obliged to catch a train.  So he proposed that White should complete the game in his absence on condition that no moves whatever should be made for Black, but only with the White pieces.  Mr. White accepted, but to his dismay found it utterly impossible to win the game under such conditions.  Try as he would, he could not checkmate his opponent.  On which square did Mr. Black leave his king?  The other pieces are in their proper positions in the diagram.  White may leave Black in check as often as he likes, for it makes no difference, as he can never arrive at a checkmate position.

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355.—­CHECKMATE!

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Strolling into one of the rooms of a London club, I noticed a position left by two players who had gone.  This position is shown in the diagram.  It is evident that White has checkmated Black.  But how did he do it?  That is the puzzle.

356.—­QUEER CHESS.

Can you place two White rooks and a White knight on the board so that the Black king (who must be on one of the four squares in the middle of the board) shall be in check with no possible move open to him?  “In other words,” the reader will say, “the king is to be shown checkmated.”  Well, you can use the term if you wish, though I intentionally do not employ it myself.  The mere fact that there is no White king on the board would be a sufficient reason for my not doing so.

357.—­ANCIENT CHINESE PUZZLE.

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My next puzzle is supposed to be Chinese, many hundreds of years old, and never fails to interest.  White to play and mate, moving each of the three pieces once, and once only.

358.—­THE SIX PAWNS.

In how many different ways may I place six pawns on the chessboard so that there shall be an even number of unoccupied squares in every row and every column?  We are not here considering the diagonals at all, and every different six squares occupied makes a different solution, so we have not to exclude reversals or reflections.

359.—­COUNTER SOLITAIRE.

Here is a little game of solitaire that is quite easy, but not so easy as to be uninteresting.  You can either rule out the squares on a sheet of cardboard or paper, or you can use a portion of your chessboard.  I have shown numbered counters in the illustration so as to make the solution easy and intelligible to all, but chess pawns or draughts will serve just as well in practice.