Amusements in Mathematics (PDF)

by Dudeney, Henry Ernest, 1857-1930

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Of course, by "royal row" is meant the row on which the king originally stands at the beginning of a game. Though, if Black plays badly, he may, in certain positions, be mated in fewer moves, the above provides for every variation he can possibly bring about.

351.?THE CRUSADER.? solution

White. 1.KttoQB3rd 2.KttakesQP

Black.

1. P to Q 4th

2. KttoQB3rd

3.KttakesKP 3. PtoKKt4th

4.KttakesB 4. Kt to KB 3rd

5. Kt takes P 5. KttoK5th

6.KttakesKt 6. KttoB6th

7.KttakesQ 7. RtoKKtsq

8.KttakesBP 8. RtoKKt3rd

9.KttakesP 9. R to K 3rd

10. Kt takes P 10. KttoKt8th

11. Kt takes B 11.RtoR6th

12. Kt takes R 12. PtoKt4th

13. Kt takes P (ch) 13. K to B 2nd

14. Kt takes P 14. KtoKt3rd

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. PtoQ4th 17. KtoR4th 18.QtoQ3rd 18. K moves 19.QtoKR3rd(mate)

tM7.KtoKt5th

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. p 9 233

352.?IMMOVABLE PAWNS.? solution

1.KttoKB3

2.KttoKR4

3.KttoKt6

4.KttakesR

5. KttoKt6

6.KttakesB

7. K takes Kt

8. KttoQB3 9.KttoR4

10. KttoKt6

11. Kt takes R

12. KttoKt6

13. Kt takes B

14. KttoQ6

15. QtoKsq

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.? solution

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 Rat 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.? solution

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!? solution

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.? solution t

picture418

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.? solution

Play as follows:?

1. R?Q 6

2. K?R7

3. R(R6)?B 6 (mate).

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

358.?THE SIX PAWNS.? solution

The general formula for six pawns on all squares greater than 2 2 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