Page:Amusements in mathematics.djvu/245

White.		Black.
14.	Kt takes P	14.	K to Kt 3rd
15.	Kt takes R	15.	K to R 4th
16.	Kt takes Kt	16.	K to R 5th
White now mates in three moves.
17.	P to Q 4th	17.	K to R 4th
18.	Q to Q 3rd	18.	K moves
19.	Q to KR 3rd (mate)
		If 17,	K to Kt 5th
18.	P to K 4th (dis. ch)	18,	K moves
19.	P to KKt 3rd (mate)

The position after the sixteenth move, with the mate in three moves, was first given by S. Loyd in Chess Nuts. 352.— IMMOVABLE PAWNS.

1.	Kt to KB 3	9.	Kt to R 4
2.	Kt to KR 4	10.	Kt to Kt 6
3.	Kt to Kt 6	11.	Kt takes R
4.	Kt takes R	12.	Kt to Kt 6
5.	Kt to Kt 6	13.	Kt takes B
6.	Kt takes B	14.	Kt to Q 6
7.	K takes Kt	15.	Q to K sq
8.	Kt to QB 3	16.	Kt takes Q
17.	K takes Kt, and the position is reached.

Black plays precisely the same moves as White, and therefore we give one set of moves only. The above seventeen moves are the fewest possible.

353.—THIRTY-SIX MATES.

Place the remaining eight White pieces thus: K at KB 4th, Q at QKt 6th, R at Q 6th, R at KKt 7th, B at Q 5th, B at KR 8th, Kt at QR 5th, and Kt at QB 5th. The following mates can then be given:—

By discovery from Q	8
By discovery from R at Q 6th	13
By discovery from B at R 8th	11
Given by Kt at R 5th	2
Given by pawns	2
Total	36

Is it possible to construct a position in which more than thirty-six different mates on the move can be given? So far as I know, nobody has yet beaten my arrangement.

354.—AN AMAZING DILEMMA.

Mr. Black left his king on his queen's knight's 7th, and no matter what piece White chooses for his pawn. Black cannot be checkmated. As we said, the Black king takes no notice of checks and never moves. White may queen his pawn, capture the Black rook, and bring his three pieces up to the attack, but mate is quite impossible. The Black king cannot be left on any other square without a checkmate being possible.

The late Sam Loyd first pointed out the peculiarity on which this puzzle is based.

355.—CHECKMATE!

Remove the White pawn from B 6th to K 4th and place a Black pawn on Black's KB 2nd. Now, White plays P to K 5th, check, and Black must play P to B 4th. Then White plays P, takes P en passant, checkmate. This was therefore White's last move, and leaves the position given. It is the only possible solution.

356.—QUEER CHESS.

If you place the pieces as follows (where only a portion of the board is given, to save space), the Black king is in check, with no possible move open to him. The reader will now see why I avoided the term "checkmate," apart from the fact that there is no White king. The position is impossible in the game of chess, because Black could not be given check by both rooks at the same time, nor could he have moved into check on his last move.

I believe the position was first published by the late S. Loyd.

357.—ANCIENT CHINESE PUZZLE.

Play as follows:—

1.	R—Q 6
2.	K—R 7
3.	R (R 6)—B 6 (mate).

Black's moves are forced, so need not be given.

358.—THE SIX PAWNS.

The general formula for six pawns on all squares greater than 2² is this: Six times the square of the number of combinations of $n$ things taken three at a time, where $n$ represents the number of squares on the side of the board. Of course, where n is even the unoccupied squares in the rows and columns will be even, and where $n$ is odd the number of squares will be odd. Here $n$ is 8, so the answer is 18,816 different ways. This is "The Dyer's Puzzle" (Canterbury Puzzles, No. 27) in another form. I repeat it here in order to explain a method of solving that will be readily grasped by the novice. First of all, it is evident that if we put a pawn on any line, we must put a second one in that line in order that the remainder may be even in number. We cannot put four or six in any row without making it impossible to get an even number in all the columns interfered with. We have, therefore, to put two pawns in each of three rows and in each of three columns. Now, there are just six schemes or arrangements that fulfil these conditions, and these are shown in Diagrams A to F, inclusive, on next page.