20 May 2011

Of boards (again), zig-zags and illegal clusters

Another very interesting little book on fairy chess by Thomas Rayner Dawson is Caissa's Wild Roses (published 1935). As the author states in his preface, this was "the first English text to give a reasonably broad outline of Fairy Chess".

The booklet starts with some remarks about the term fairy chess in comparison to normal chess. What are the characteristics of normal chess? Firstly, you have the playing space. It is a plane board with eight ranks and eight files. Secondly, there are the six different types of pieces: king, queen, rook, bishop, knight, and pawn. Each of them has its own style of moving. Thirdly, miscellaneous limitations on move freedom exist, e.g. the alternation of White and Black moves, capture, pawn promotion, castling, check, checkmate, various types of draws. Dawson concludes: "From this point of view, normal chess is evidently an arbitrary group of elements selected from an infinity of analogous geometrical conceptions. Fairy Chess comprises the study of all such elements, taken in arbitrary groups at will."

If you wanted to be absolutely correct and take the strictly formal approach, you'd have to define and list all elements of the respective fairy chess field that is relevant for a particular chess problem. Of course, there is a better way of handling that. The elements of the normal chess are considered as a basis and only the changes are mentioned. For instance, you use a new set of rules, leaving the board and the piece types unchanged. Or you might introduce a new type of piece and only modify the normal rules where necessary.

Dawson ends his comments on fairy chess with the following statement as one of the answers to the question why it finds enthusiastic devotees: "Fairy Chess offers an infinite field for the expression of Man's scientific and artistic imagination and adds new glory to his intellectual achievements."

In an earlier post featuring a larger board, I already mentioned the necessity of using a different board depending on the demonstrated theme, for instance. Interestingly, you can read something similar in Dawson's booklet: "The rational principles in studying chess boards as elements for variation are (i) the size of the board must be in unity with the problem representation; and (ii) the specific nature of each board demands the discovery of specific themes peculiar to such board (Problemist, March, 1928)."

The first example I picked for you shows a board with changing width in each phase, leading to different play, of course. Also, the problems 3 and 4 use a non-standard board. More of interest, though, is the concept of zig-zags featured in Nos. 2—4. Dawson himself admits that it is almost impossible to exactly define this term, as it rather covers a type of play than a type of problem (emphasis added by me): "The zig-zag involves the permutation of men of one or both colours, in general with abandonment of the principle of alternate White and Black moves, but not necessarily so." By the way, in one of my previous posts, I already showed an example of a zig-zag. Finally, you get to see three problems introducing illegal clusters. An illegal cluster is an illegal position which becomes legal upon removal of a single (arbitrary) unit, excluding kings.

  1T. R. Dawson  
The Problemist, 1930
  inaccessible squares a1 to a6
a) Diagram
b) cut off h-file
c) further cut off g-file
d) further cut off f-file
e) further cut off e-file
f) further cut off d-file

  2T. R. Dawson  
Eskilstuna.Kuriren, 1921
After every move all 4 men must
be guarded. Interchange rooks, with bishops back, in 28

  3T. R. Dawson  
Bolton Football Field, 1910
No man ever guarding another, play 21. Ka4

  4T. R. Dawson  
L'Eco degli Scacchi, 1918
No man ever guarding another, play 22. Ka4

  5T. R. Dawson  
The Problemist Fairy Chess Supplement, 1933
Add black rook and black bishop to form an illegal cluster.

  6T. R. Dawson  
The Problemist Fairy Chess Supplement, 1933
a) two
b) three
black pawns to form an illegal cluster.

  7T. R. Dawson  
The Problemist Fairy Chess Supplement, 1933
Add black rook and
a) one
b) two
black pawn(s) to form an illegal cluster.
c) like b) with position rotated
by 180 degrees

1 a) 1. Qh1! N~ / f4 2. Qh8 / Qxh3#
b) 1. Qd1! f4 2. Qg4#
c) 1. f4! exf3 e.p. 2. Qxf5#
d) 1. Qxe4! Kd7 2. Qe6#
e) 1. Qcl! Kd7 2. c8=Q#
f) 1. Ka7! Kxc7 2. Qc1#
2 1. Bc1, 2. Bb3, 3. Ba3, 4. Bd1, 5. Bb4, 6. Ba5, 7. Rc1, 8. Bc3, 9. Rc2, 10. Rac1, 11. Be2, 12. Be1,
13. Bc4, 14. Bd2, 15. Ra2, 16. Rcc2, 17. Bc1, 18. Ba3, 19. Rc1, 20. Raa1, 21. Bf1, 22. Rcb1, 23. Bb5, 24. Bc1, 25. Ba4, 26. Bb3, 27. Ba2, 28. Bb2.
3 1. Kc1, 2. Rd4, 3. Rd3, 4. Qa4, 5. Kb1, 6. Rd2, 7. Qc4, 8. Ka1, 9. Qb3, 10. Rd4, 11. Qc2, 12. Rb4,
13. Qd3, 14. Ka2, 15. Qd1, 16. Rc4, 17. Ka3, 18. Qb1, 19. Rd4, 20. Rd2, 21. Ka4
4 1. Kc1, 2. Qb4, 3. Kd1, 4. Qb2, 5. Bc4, 6. Qa3, 7. Kd2, 8. Qa1, 9. Bb3, 10. Kd3, 11. Qcl, 12. Ba4,
13. Qb2, 14. Kc4, 15. Bd1, 16. Qa3, 17. Bc2, 18. Qa1, 19. Kb4, 20. Bd3, 21. Qc1, 22. Ka4
5 Add bRg4 and bBh8.
If you remove the rook, the last move was Ng7-e6+. Without the bishop, it was Nf4-e6+. Finally, taking away the knight allows Rg7-g4+ as last move.
6 a) Add black pawns on b4 and d4.
b) Add black pawns on a6, a7 and b7.
The solution to b) is totally different, quite surprising.
7 a) Add bRc5 and bPc4.
b) Add bRe3, bPd2, bPd3. Here, we see an en passant capture after removal of the bPd2: the last move must have been e4xd3 e.p., then.
c) Add bRf8, bPf7, bPh6.


seetharaman said...

Please check the answer to puzzle 5. Black king is already in g8? so where to add the black rook?

Answer to Question 6.b should add black pawns a7,a6 and b7.

bernoulli said...

Thank you for your notes.
I corrected the errors. The diagram of No. 5 was also wrong.