Retroanalysis

Monochrome Play with Grasshoppers

The idea of monochrome play, which I discovered in composing this Fairy Retro with Grasshoppers, was later taken up by other composers in the form of ‘Monochrome Chess’ in which the rule is taken as a fixed law. This leads to complex retroanalytical possibilities, and to strange positions, where for example the kings can stand on adjacent squares of opposite colour without checking. However, the idea in the form in which I intended it, i.e. as a condition on play rather than a law, has not hitherto been taken up in other compositions.

This composition grew out of the simple initial observation that a black Grasshopper placed on g1, between white King and Rook, with the white pawns still in place on efgh2, could only escape via d1, since the other moves to e3 and g3 check the white King.

Solution: (a) The odd move was Gg1-d1. (b) Rooks taken: a8-e6, h8-h8, a1-g3, h1-h5. (c) Last move Gf7×Rh5‡.

Analysis: No knight has moved. Ps that promote must make at least 4 captures en route. WK has escaped from e1 by 00 after Bf1 and Ng1 were captured. Last move must have been Gf7×h5‡. This last captured man plus Bf1 and 6 visible white men leave 8 that were captured by the 2 black Ps that promoted to Gs, including Ng1. Since both black Gs are on white squares, the G that appeared at g1 must have made the one colour-change move, and it must have gone to d1 to avoid checking the WKe1. Nb8 was captured by promoted black-square G or Q before Ra8 got out to become one of the other white P captures (on way to g8) so Rh8 died at home. Each R is restricted to a quarter of the squares of the board.

Comments: "Very fine retro with many hidden points" (J.D.Beasley). "Very beautiful, fully justifies its ad hoc stipulation" (R.Peele). "Colour-bar adds a new dimension. Not often one can prove Pa4×b4 e.p. occurred with all the nearby squares now unoccupied" (C. R. Flood). Prize in Fairy Retro Award (November-December 1977, p.181). "A profound and difficult study in an entirely new medium. The monochrome rule transforms normal retro reasoning and introduces a new basis for e.p. uncapture" (D. Nixon).

Retroanalysis in Edge Chess

This problem is dedicated to the memory of J. E. Driver, inventor of the Edgehog.

In Edge Chess only moves to or from the edge cells are permitted. Here the 'or' is inclusive (I-type), that is moves from edge to edge are permitted.

Solution: Black may castle either side. White may not.

Analysis: There are five available BP captives: WQ,2S,B,gP, and two WP captives BQ,S. Cannot retract BPb3xa2 because then also BPa4xb3 and another bxa leads to six BP captures. Hence WP caps at a3,b7. The men at c8,b7,b5 cannot be retracted until BPa2 is home, so BSa7 came from c6 and BBc6 from h1, disturbing WR. Three BP caps at b5,a6,h6 and two at g2 since WPg2 must be taken first to allow BBc6 to h1 and some other W man later by BPg2. The dark-square WB was captured at h6 and so had to disturb WRa1 to get out (BPg7 preventing it going to h8). Finally since we cannot prove that WBc8 disturbed Ra8 rather than Rh1 and that BBc1 disturbed Rh8 rather than Ra1, Black gets the benefit of the doubt.

Comments: "Novel Bishop difficulties arise from Edge Chess" C. R. Flood. "Complex and fascinating position" R. M. W. Musson. "A masterpiece. This and F517R have completely broken my resistance to retroanalysis" R. W. Smook. "I like the precise logic of this and F520R" T. Marlow. Special mention in the Fairies Award July 1980 pp.63-64. "Unquestionably the best of the 'Fairy retros' in 1979. An original and unusual problem, and a worthy tribute to J. E. D. to whose memory the problem is dedicated" R. M. W. Musson.

Chess in Disguise Revelation

In Chess in Disguise, invented by John Beasley, each player starts with K and 8P in usual positions, plus Q, R, S, white-square and black-square Bs, R+S, B+S, all disguised as draughtsmen (shown here by rotated pawns) whose identities in a game must be deduced from their moves and checks, or revealed on capture.

Solution: a1=S, c1=B+S, c5=S, c8=B, d1=R+S, d4=B, e1=R, e8=R+S, g1=B, h1=Q, h5=B, h8=B+S.

Analysis: c8=B, g1=B (not e1 since this would prevent WK retracting to e1), h5=B, d4=B (not f8 since this would prevent BK retracting to e8), e1=R (W therefore castled), h1=Q (since a1, c1, d1 must be S-movers and BR cannot reach h1), f8=R (black also castled). These 7 deduced from retroanalysis alone. Neither K in check, hence h6=Q, d1=R+S. For black to mate we need a1=S, c1=B+S (for c1xd2 mate). For white to mate we want e8=R+S, h8=B+S (for h8xf7 mate). This leaves just c5=S.

Comments: "Logic is all! Not for nothing does composer anagrammatize as "Jig-spells". R. Brain.

Added Men Retroanalysis

Solution: Add WKd5, BKf4 for Black Qd4 mate, or White fxe6 e.p. mate.

Analysis: Black is missing RNPP and White QBB. If black moved last cannot retract BKg5 Rg7(xg6)+ because WP caps balance missing black men; nor BPe6/d6(xQ) because WBc1 died at home and WBf1 runs on light squares, so BPd6/e6 not possible. Thus can only retract BPe5-e7. All 8 BQ retractions into check.

Comments: "When does the penny drop? Deserves to become well-known" R. M. W. Musson.

Retractor

This composition doesn't really involve retroanalysis, just backward play. It is probably the only retractor I have composed.

Solution:
(a) Retract Kb5xQa5 for Kc4 Qb4 mate.
(b) Retract Pe5xQd4 for Rb5 Qa7 mate.
(c) Retract Rb5xQd5 for Rc5 Qxc5 mate.

Proof Game in Antipodean Chess

I invented Antipodean Chess as an antidote to Circe Chess back in the first issue of Chessics in 1976. Unfortunately some chess problem editors now refer to it as "Antipodean Circe" which annoys me considerably. In Antipodean Chess a captured unit is reborn on the square a (4,4) leap away, unless that square is occupied.

"RI" stands for "Rex Inclusive" which means the rule also applies to the kings. Thus the white King is not in check in the diagram position, though it would be if square a5 was occupied.

The stipulation PG 9.0 means: play a game, from the usual opening position, to reach the diagram position on Black's 9th move. Such a sequence of moves is known as a Proof Game since it shows the given position is reachable by legal moves. The art is to construct a position in which the sequence of moves is uniquely determined.

Solution: The play, starting from the opening position is: 1-3. a6 c3 4.a*b7(f3) f*g2(c6) 5.Ra6 Qa5 6. c7 Qa1 7. Ra4 c*d2(h6) 8. h*g7(c3) c*b2(f6) 9.f*e7(a3) a2.

Comments: "Extremely entertaining, with two chain reactions of reborn P capturing P; avoidance of a check on wK provides a dual-free solution" (F. Moralee). Several changes of move order possible, but for need to keep a5 empty after black c*d2" (T. Marlow). Very original; diagram initially sent me cross-eyed, but actually not too difficult" (C. C. Frankiss). "The Turton by wR and bQ adds interest" (C. Lytton). The idea of interchanging Antipodean Pawns goes back to Chessics issue 2, p.7.