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 nonstandard board. More of interest, though, is the concept of zigzags 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 zigzag 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 zigzag. 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.







Solutions:
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 Ng7e6+. Without the bishop, it was Nf4e6+. Finally, taking away the knight allows Rg7g4+ 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. 
2 comments:
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.
Thank you for your notes.
I corrected the errors. The diagram of No. 5 was also wrong.
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