The Water Wheel

"The ideas of most of the mansubas were taken over and then superiorly developed and realized by the modern problemists [...]. However, there was one idea that could not be brought to fruition until over 1000 years after its birth!" (V. Petrovici, Planeta Sah, 1989)

"The Water Wheel Mansuba, a marvelous concept that has not yet been fully expressed under the modern rules of chess, was presented as a chess position of ancient times, supposedly found carved in stone," writes F. Bondarenko in his book Gallery of Chess Studies (1968). Three years later, the following study is published:

L. Shilkov
Shahmaty v SSSR
1971
Correction by A. Rusz (2026)
White wins

[FEN "bqB2n1r/1P2p2p/4p3/2P1RP1k/4Pr1P/pP3n2/Kp3Np1/b1B2N1R w - - 0 1"]

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1. Ng3+ Kh6 2. Ng4+ Kg7 3. Nh5+ Kf7 3... Kg8 4. Nh6# 4. Nh6+ Ke8 5. Ng7+ Kd8 6. Nf7+ Kc7 7. Ne8+ Kc6 8. Nd8+ Kb5 9. Nc7+ Kb4 9... Ka5 10. Nc6#; 9... Qxc7 10. bxa8=Q +- 10. Nc6+ Kc3 11. Nb5+ Kd3 11... Kc2 12. Nb4# 12. Nb4+ Ke2 13. Nc3+ Kf2 14. Nd3+ Kg3 15. Ne2+ Kg4 16. Nf2+ Kh5 17. Nxf4+ Kh6 18. Ng4+ Kg7 19. Nh5+ Kf7 20. Nh6+ Ke8 21. Ng7+ Kd8 22. Nf7+ Kc7 23. Ne8+ Kc6 24. Nd8+ Kb5 25. Nc7+ Kb4 26. Nc6+ Kc3 27. Nb5+ Kd3 28. Nb4+ Ke2 29. Nc3+ Kf2 30. Nd3+ Kg3 31. Ne2+ Kg4 32. Nf2+ Kh5 33. Ng3#

The black king and the two chasing knights follow this path twice:

This study was published with the following initial position in Shakhmaty v SSSR 1971/1:

To eliminate the 7.cxb6+ dual, I have moved the black pawn from b6 to a3.

Let's see a mansuba with the same idea. The following position is from a manuscript kept in the British Museum, London (Add MS 7515), written in 1257. This manuscript is a compilation of earlier chess books from the 9th and 10th centuries.

Here is the diagram (I have reversed the colours, in the original, black was going to checkmate "red"):

The bishop ("alfil") and the queen ("ferz") had different movements back then. The alfil moved exactly two squares diagonally, jumping over the square between (which means d7 is attacked by the Af5). The ferz moved just one square diagonally (so the black king is not in check yet, but the c7 square is attacked by Fb8).

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Study 187

Happy New Year 2021!

Árpád Rusz
Internet (RCS blog)
2020
Draw

1. c8=Q f1=Q 2. Qc3+ Qd3 2... Rd3 3. Qxe5+ Kd2 4. Qb2+ Ke3 5. Qe5+ perpetual check

3. Qxe5+ Kf3 4. Qh5+ Kg2 5. Qg5+ Kf2 6. Qf6+ Kg1 7. Qg7+ Kh2 7... Rg2 8. Qa1+ Kf2 9. Qa2+ Kg3 10. Qg8+ Kh2 11. Qh8+ Kg1 12. Qa1+ perpetual check

8. Qh6+ Kg3 9. Qg5+ Kf2 10. Qf6+ Ke3 10... Kg1 11. Qg7+ perpetual check

11. Qe5+ Kf3 12. Qh5+ Ke4 13. Qh1+ Kd4 14. Qa1+ Kd5 15. Qa8+ Ke5 16. Qh8+ Ke4 17. Qh1+ perpetual check

Study 180

Árpád Rusz & Pavel Arestov
Iriarte MT
2019
- section B1 -
1st/2nd Prize

White wins

1. d4! The start of the first systematic movement. (The "elevator" goes up.) 1. Kxa5? Kxd3 = The black rook will get behind the white pawn on the g-file because the white king cannot find shelter from horizontal checks. 1... Kd3 2. d5 2. Kxa5? Kxd4 3. Kb6 Rh6+ = 2... Kd4 2... Rh4+ 3. Kxa5 Rg4 4. Kb6 (4. d6? Rg6 5. Kb5 Kd4 =) 4... Kd4 5. d6 Kd5 6. Kc7 Ke6 7. Re8+ +- 3. d6 3. Kxa5? Kxd5 4. Kb5 Kd4! 5. Kb4 Kd5 6. Kb5 Kd4 = 3... Kd5 4. Kxa5 Kxd6 5. Kb6! Now the white king can hide from horizontal checks. 5... Kd5 6. Kc7

6... d6 The start of the second systematic movement. (The "elevator" goes down.) 6... Ke6 7. Re8+ +- 7. Kb6! 7. Kd7? Ke5 8. Re8+ Kf6 = The white pawn is pinned. 7... Kd4 The black king should always stay in the shadow of the d-pawn avoiding vertical checks. 8. Kc6 8. Kb5? Rh5+ 9. Kc6 Rg5 10. Kxd6 Rg6+ 11. Ke7 Ke5 12. Kf7 Rf6+ = 8... d5 9. Kb5! Kd3 10. Kc5 d4 11. Kb4! Kd2 12. Kc4 d3 13. Kb3! Kd1 14. Kc3 14. Kb2? d2! = mutual zugzwang (14... Rh2+? 15. Kc3 d2 16. Rd8 Rg2 17. Rxd2+! +-) 14... d2 15. Kb2! mutual zugzwang 15... Rh5 15... Ke2 16. Re8+ +- 16. Rb8! +- 16. Rd8? Rb5+ =

The first version of this study was a miniature: Study 173

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Study 173

Árpád Rusz
Iriarte MT
2019

White wins

1. g7 1. Rd8? Ra1! 2. Rxd6 Ra7+ = 1... Rh7 2. Rg8 Kxd5

systematic movement

3. Kb6! 3. Kd7? Ke5 4. Re8+ Kf6 = 3... Kd4 3... Ke6 4. Re8+ +- 4. Kc6 4. Kb5? Rh5+ 5. Kc6 Rg5 6. Kxd6 Rg6+ 7. Ke7 Ke5 8. Kf7 Rf6+ = 4... d5 5. Kb5 Kd3 6. Kc5 d4 7. Kb4 Kd2 8. Kc4 d3 9. Kb3 Kd1 10. Kc3! 10. Kb2? d2 = mutual zugzwang 10... d2 11. Kb2 mutual zugzwang 11... Rh6 11... Ke2 12. Re8+ +- 12. Rb8! +- Switchback 12. Rd8? Rb6+ =

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Pavel Arestov proposed a new version.

Study 93

Árpád Rusz
Marwitz-100 MT, 2016
Special Prize
- version -

White wins

Now I prefer this more economical initial position of Study 93a. The main line and the two tries all feature different systematic movements!

1st try: 1.f8Q? Ra7+ 2.Kb8 Rab7+! 2...Rhb7+? 3.Kc8 Rc7+ 4.Kd8 Rd7+ 5.Ke8 Re7+ 6.Qxe7+– 3.Kc8 Rbc7+ 4.Kd8 Rcd7+ 5.Ke8 Rde7+ 6.Qxe7 Rxh8+ 7.Kd7 h2 8.Qf7+ Kb1 9.Qb3+ Kc1= 9...Ka1? 10.Qc3++–

2nd try: 1.Qxg7? Rxg7 2.f8Q h2! 3.Qxf3

3...Rg8+!! Paradoxically, black lets the white king to escape from the eight rank! The immediate 3...Rg1? loses because of a Queen staircase on the a and b-files from b3 to b8! 4.Qb3+ Ka1 5.Qa3+ Kb1 6.Qb4+ Ka1 7.Qa5+ Kb1 8.Qb6+ Ka1 9.Qa7+ Kb1 10.Qb8++– 4.Kb7 Rg1! Another check would be fatal: 4...Rg7+? 5.Kc8!! Back to the 8th rank! (5.Kc6? Rg1 6.Qb3+ Ka1 7.Qa3+ Kb1 8.Qb4+ Ka1 9.Qa5+ Kb1 10.Qb6+ Kc1!=) 5...Rg8+ 6.Kd7!+– 5.Qb3+ Ka1 6.Qa3+ Kb1 7.Qb4+ Ka1(2) 8.Qa5+ Kb1 9.Qb6+ Ka1(2) 10.Qa7+ Kb1(2)=

Main: 1.Qxh7! Rxh7

2.f8Q f2! 2...h2 6.Qg8++– 3.Qxf2 3.Qg8+? Ka1! 4.Qxh7 f1Q=; 3.c4? Rh8! 4.Qxh8 f1Q= 3...h2 4.c4+ Kb3 5.Qf3+ Kb4! 5...Kxc4 6.Qe4++– 6.Qh1 Kc5!

The plan that looks logical now is starting to move with the white king towards the rook. But it doesn't work yet! While the black king is on c5 the rook can leave the seventh rank (e.g. by moving to h5). 7.Qd5+ Kb4 8.Qd2+ Kc5 9.Qf2+ Kb4 10.Qb2+ Kc5 11.Qb5+ Kd4 12.Qd5+ Kc3 13.Qh1 Kd4 The black king is not on c5 so the white king can make a move towards the rook! 14.Kb8! The first step. 14...Kc5 Back to c5... White needs to repeat the manoeuvre to gain a tempo for another king move.

15.Qd5+ Kb4 16.Qd2+ Kc5 17.Qf2+ Kb4 18.Qb2+ Kc5 19.Qb5+ Kd4 20.Qd5+ Kc3 21.Qh1 Kd4 22.Kc8! The second step. 22...Kc5

23.Qd5+ Kb4 24.Qd2+ Kc5 25.Qf2+ Kb4 26.Qb2+ Kc5 27.Qb5+ Kd4 28.Qd5+ Kc3 29.Qh1 Kd4 30.Kd8! The third step. 30...Kc5

31.Qd5+ Kb4 32.Qd2+ Kc5 33.Qf2+ Kb4 34.Qb2+ Kc5 35.Qb5+ Kd4 36.Qd5+ Kc3 37.Qh1 Kd4 38.Ke8! The fourth step. 38...Kc5

39.Qd5+ Kb4 40.Qd2+ Kc5 41.Qf2+ Kb4 42.Qb2+ Kc5 43.Qb5+ Kd4 44.Qd5+ Kc3 45.Qh1 Kd4 46.Kf8! The fifth step. 46...Kc5

47.Qd5+ Kb4 48.Qd2+ Kc5 49.Qf2+ Kb4 50.Qb2+ Kc5 51.Qb5+ Kd4 52.Qd5+ Kc3 53.Qh1 Kd4 54.Kg8! +- The last step along the 8th rank.

The white king will finally escape from the last rank. White has a winning position. Notice that this was the 50th move since the last capture or pawn move (4.c4+), so according to the FIDE rules, this position would be a draw! Fortunately, endgame study composition codex doesn't care about that artificial "draw by 50 moves" rule!

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Excelsior 5

O. Pervakov
Tidskrift for Schack
1993
2nd Honourable Mention - version

White wins

1. d3+! Kf1! 1... axb4 2. h7 +- 2. Kh2 Rxh6+ 3. Kg3 Ra6 4. Bb5! Rxa7 5. d4+ Kg1 6. Bc5! Ra8! 7. d5+ Kh1 8. Bc6! 8. d6? Be4! = 8... Ra6 9. d6+ 9. Bb7? Rd6! = 9... Rxc6 10. d7! Rxc5 11. d8=Q +-

Excelsior 2

V. Korolkov
Thèmes 64
1959

White wins

1. Be7+ Kg3 2. Bxf8 Qxf8 3. gxh3+ Kh4 4. hxg4+ Kg5 5. gxh5+ Kh6 6. hxg6+ Kg7 7. gxh7+ Kh8 8. Rg8+ Qxg8 9. hxg8=Q+ Kxg8 10. Rb1! Nc7 11. Rb8+ Kf7 12. Rb7 +-

Study 101

Á. Rusz
RCS blog
2016
- after S. Chimedtzeren -

White wins

All four corners of the board are empty in the starting position. 1. Rb7+ Ka8 The first move to a corner square. 2. Be4! (Thematic try: 2. Bh1?? Qc2+ -+) 2... Qe3! (2... Qd4+ 3. Rb4+ +-) 3. Bh1! The second move to a corner square. 3... Qe8+ Roman Theme. The black queen cannot reach the c2 square anymore so it has to find another square to give a check.4. Ka3 Qf8+ 5. Ka2 Qg8+ 6. Ka1! The third move to a corner square. 6... Qh8+ The fourth move to a corner square. Now all four corners are full!

7. Kb1 h2 8. Rh7+ Kb8 9. Rxh8+ +- The last move to a corner square. During the main line, four pieces have moved to a corner square!

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Related studies: Study 101a

Study 101a

S. Chimedtzeren
L'Italia Scacchistica
1975
2nd Prize

White wins

1. Be4! 1. Bh1?? Qc2+ 2. Rb3+ Ka7 -+ 1... Qe3 2. Bh1! Qe8+ 3. Ka3 Qf8+ 4. Ka2 Qg8+ 5. Ka1 Qh8+ 6. Kb1! +-

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Related studies: Study 101

Study 93a

Árpád Rusz
Marwitz-100 MT, 2016
Special Prize
- version -

White wins

1.Rxa3+! 1.Qxh7? Rg5 2.Rxa3+ Qxa3+ 3.Kb7 Rb5+=; 1.f8Q? Qa5+ 2.Kb7 Qb5+ 3.Ka7 Qa5+ perpetual check 1...Qxa3+ 1...Kxa3 2.Qxh7 Rg5 3.Qd3++– 2.Kb8! 2.Kb7? Rgxg7 3.Rxa3+ Kxa3–+ 2...Qxa8+ 3.Kxa8 Rgxg7! Capturing the Queen leads to two echo positions: 3...Rxh8+ 4.Bxh8 h2 5.f8Q h1Q 6.Qf7+ Kb1 7.Qb3+ Kc1 8.Qb2+ Kd2 9.Qc3+ Ke2 (9...Kd1 10.Qa1++– echo position 1)

10.Qd3+ Ke1 11.Bc3+ Kf2 12.Qd2+ Kg3 13.Be5+ Kg4 14.Qf4+ Kh5 15.Qf5+ Kh6 16.Qf6+ Kh5 17.Qh8++– echo position 2

So back to the main line after black’s third move we have the following critical position on the board:

This could be a more economical starting position of the study. The main line and the two tries all feature different systematic movements!
Try1: 4.f8Q? Ra7+ 5.Kb8 Rab7+! (5...Rhb7+? 6.Kc8 Rc7+ 7.Kd8 Rd7+ 8.Ke8 Re7+ 9.Qxe7+–) 6.Kc8 Rbc7+ 7.Kd8 Rcd7+ 8.Ke8 Rde7+ 9.Qxe7 Rxh8+ 10.Kd7 h2 11.Qf7+ Kb1 12.Qb3+ Kc1= (12...Ka1? 13.Qc3++–);
Try2: 4.Qxg7? Rxg7 5.f8Q h2! (5...Rg3? 6.Qh6! Kb2 (6...f2 7.Qe6+ Kb1 8.Qb6++–) 7.Qd2!+–) 6.Qxf3

6...Rg8+!! Paradoxically, black lets the white king to escape from the eight rank! (The immediate 6...Rg1? loses because of a Queen staircase on the a and b-files from b3 to b8! 7.Qb3+ Ka1 8.Qa3+ Kb1 9.Qb4+ Ka1 10.Qa5+ Kb1 11.Qb6+ Ka1 12.Qa7+ Kb1 13.Qb8++– ) 7.Kb7 Rg1! (7...Rg7+? 8.Kc8!! Back to the eight rank! (8.Kc6? Rg1 9.Qb3+ Ka1 10.Qa3+ Kb1 11.Qb4+ Ka1 12.Qa5+ Kb1 13.Qb6+ Kc1!=) 8...Rg8+ 9.Kd7!+–) 8.Qb3+ Ka1 9.Qa3+ Kb1 10.Qb4+ Ka1(2) 11.Qa5+ Kb1 12.Qb6+ Ka1(2) 13.Qa7+ Kb1(2)=
Main: 4.Qxh7! It is a paradox that white captures the rook only after black managed to protect it.4...Rxh7

This could be an even more economical starting position. My feeling is that a lot would be lost with this simplification. 5.f8Q f2! 5...h2 6.Qg8++– 6.Qxf2 6.Qg8+? Ka1! 7.Qxh7 f1Q=; 6.c4? Rh8! 7.Qxh8 f1Q= 6...h2 7.c4+ Kb3 8.Qf3+ Kb4! 8...Kxc4 9.Qe4++– 9.Qh1 Kc5!

The plan that looks logical now is starting to move with the white king towards the rook. But it doesn't work yet! While the black king is on c5 the rook can leave the seventh rank (e.g. by moving to h5). 10.Qd5+ Kb4 11.Qd2+ Kc5 12.Qf2+ Kb4 13.Qb2+ Kc5 14.Qb5+ Kd4 15.Qd5+ Kc3 16.Qh1 Kd4 The black king is not on c5 so the white king can make a move towards the rook! 17.Kb8! The first step. 17...Kc5 Back to c5... White needs to repeat the manoeuvre to gain a tempo for another king move.

18.Qd5+ Kb4 19.Qd2+ Kc5 20.Qf2+ Kb4 21.Qb2+ Kc5 22.Qb5+ Kd4 23.Qd5+ Kc3 24.Qh1 Kd4 25.Kc8! The second step. 25...Kc5

26.Qd5+ Kb4 27.Qd2+ Kc5 28.Qf2+ Kb4 29.Qb2+ Kc5 30.Qb5+ Kd4 31.Qd5+ Kc3 32.Qh1 Kd4 33.Kd8! The third step. 33...Kc5

34.Qd5+ Kb4 35.Qd2+ Kc5 36.Qf2+ Kb4 37.Qb2+ Kc5 38.Qb5+ Kd4 39.Qd5+ Kc3 40.Qh1 Kd4 41.Ke8! The fourth step. 41...Kc5

42.Qd5+ Kb4 43.Qd2+ Kc5 44.Qf2+ Kb4 45.Qb2+ Kc5 46.Qb5+ Kd4 47.Qd5+ Kc3 48.Qh1 Kd4 49.Kf8! The fifth step. 49...Kc5

50.Qd5+ Kb4 51.Qd2+ Kc5 52.Qf2+ Kb4 53.Qb2+ Kc5 54.Qb5+ Kd4 55.Qd5+ Kc3 56.Qh1 Kd4 57.Kg8! +- The last step along the eight file.

The white king will finally escape from the last rank. White has a winning position. Notice that this was the 50th move since the last capture or pawn move (7.c4+), so according to the FIDE rules, this position would be a draw! Fortunately, endgame study composition codex doesn't care about that artificial "draw by 50 moves" rule!

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Related study: Study 93.

Study 85

Árpád Rusz
3rd UAPA Ty
2015
4th Honourable Mention

White wins

1. c7! 1. Bxe7+? Kxe7+ 2. c7 Kd7! (2... Bxa1? 3. c8=Q +-) 3. Kb7 Bxc7 -+ 1... Kd7 2. Bxe7 Bxc7+ 3. Kb7

systematic movement R/B

3...Be5! 3... Kxe7 4. Kxc7 +-; 3... Bxa5 4. Rxa5 Bc6+ 5. Kb6 Kxe7 6. Kxc6 +- 4. Re1! Bg3! 5. Rg1! 5. Re3? f4 = 5... Bh2 5... Bf2 6. Rg2! +- (6. Rf1? c3! 7. Rxf2 c2 8. Nb3 Kxe7 =) 6. Rh1! 6. Rg2? Bc7! 7. Bxb4 Bxa5 8. Bxa5 Bc6+ = 6... Bc7! 7. h5!! 7. Bxb4? Bxa5 8. Bxa5 Bc6+ =; 7. Ra1?! Be5 positional draw 7...gxh5 7... Bxa5 8. h6 +- 8. Ra1 Be5 8... b3 9. Bb4 f4 10. d3! +- 9. Re1 Bg3 10. Re3! f4 11. Re5 f3 12. Rxb5 f2 13. Rf5 +-

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Study 75

Árpád Rusz
Magyar Sakkvilág
2013
- version -

White wins

1.axb4+ Kxa4 1...cxb4 2.Kb3 bxa6 3.Rbxd6! exd6 4.Rh5+ d5 5.Rxd5# 2.bxc5 Rxa6 We have reached the starting position of the original 2013 version. 3.cxd6! 3.Rxa6+? bxa6 4.cxd6 exd6=; 3.Rxb7? Nxb7= 3...Rxb6 3...exd6 4.Rxb7+- 4.dxe7! 4.Rh4+? Kb5 5.dxe7 Ra6+ 6.Kb3 Ra8 7.Rh8 Ng6! 8.Rxa8 Nxe7= 4...Rxh6 5.exf8Q 5.e8Q+? Ka5! (5...Rc6? 6.Qa8+! Kb5 7.Qxb7+ Rb6 8.Qd5+ Ka6 9.Qa8++-) 6.Qxf8 Rc6 7.Qa8+ Kb6= fortress 5...Ra6! 5...Rc6 6.Qa8++- 6.Qc5 Rb6! cyclic zugzwang 1 WTM. 6...Ra5 7.Qc4#

WTM

This analysis uses the term "Cyclic Zugzwang" which is the generalization of the common 3-move (or 5 ply) long triangulation to pass the move to the weaker side. If the stronger side is to move in a "cyclic zugzwang" position, it wins more slowly than with the other side to move and in order to win, the stronger side can be forced to visit the same position but with the other side to move. So now white has to pass the move to the black. There are some R/Q corresponding squares: b6/c5, b5/c7, b4/e7 and it seems like the queen also has the e5 and d6 squares as possible "tempo squares".

7.Ka1!! 7.Qxb6? stalemate; 7.Qe5? Using e5 as a tempo square fails: 7...Kb4!= (After 7...Rb5? white would win by using the corresponding squares 8.Qc7! Rb4 9.Qe7! Rb6 10.Qc5!+-) 7...Rb5 7...Ra6 8.Kb1! (8.Kb2? Rc6! 9.Qa7+ Ra6 10.Qxb7 (10.Qc5 Rc6 perpetual attack) 10...Rb6+! 11.Qxb6 stalemate) 8...Rc6 9.Qa7+ Ra6 10.Qxb7+- 8.Qc7! 8.Qa7+? Kb4 9.Qd4+ Ka5 10.Ka2 Ka6 11.Ka3 Ra5+ 12.Kb3!? Rb5+ (12...b6? 13.Qd7 Rc5 14.Kb4 mutual zugzwang 14...Ra5 15.Qc8+ Ka7 16.Qc7+ Ka6 17.Qb8+-) 13.Kc4 Ra5!= (13...Rh5? 14.Qd3! Ka7 15.Qe3+ Ka6 16.Qe2! b5+ 17.Kb3 Rh3+ 18.Kb2 Rh4 19.Qe6+ Ka5 20.Qe1++-) 8...Rb4 9.Ka2 Rb5 cyclic zugzwang 2 WTM 9...Rb3 10.Qc2+- 10.Qd6! This is the right tempo square! 10.Qe7? Ka5= 10...Rb4 10...Rb3 11.Qd1+-; 10...Ka5 11.Ka3+- 11.Qe7! cyclic zugzwang 3 BTM 11.Qf8?! Ka5 12.Qc5+ Rb5 13.Qa7+ Kb4 14.Qa3+ Kc4 15.Qc1+ Kb4 16.Qc7 Ka4 17.Qd6 Rb4 is only waste of time 11...Rb3 This defence now becames possible because there are no more pins along the a4-d1 diagonal (there is no e0–square on the board)! 11...Rb5 12.Qa3#; 11...Rb6 12.Qc5! cyclic zugzwang 1 BTM. White finally managed to pass the move to the black.

BTM

12...Rb4 13.Qa7++-

Back to the main line we have this position:

12.Qf8! +- This second "Q-promotion on f8" wins! The other "promotion" 12.Qe8+?! Rb5 13.Qd8 Ra5 14.Qb6 Rb5 15.Qc7 Rb4 16.Qe7 Rb3 17.Qf8 is only waste of time.

The c5->d6->e7->f8 "road" is visited both by the white pawn and the promoted white queen!

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