a) If Black has made the captures e.p., then the retraction d4xe3 e.p. is not possible as e2-e4 would not defend against the check by bBh6. Retraction from the other side gives 1.h4xg3 e.p g2-g4 2. g4xf3 e.p. f2-f4 3.f4xe3 e.p, whereby the previous move by White has been e2-e4. However, this is an illegal position. The three missing white pieces were captured by black pawns. But R(h1) could not get out to be captured.
b) If White has made the captures e.p., then the retraction e5xd6 e.p. is not possible as the black king would have been in check. The attempted retraction 1.a5xb6 e.p. b7-b5 2.b5xc6 e.p c7-c5 3.c5xd6 e.p .leads to.an illegal position. The three missing black pieces have been captured by white pawns, but B(c8) could not escape to be captured.
Solution: The three consecutive e.p. captures have been made by the pawns a6, b6 and c6, giving unique retractions.
a) If Black has made the captures e.p., then the retraction d4xe3 e.p. is not possible as e2-e4 would not defend against the check by bBh6. Retraction from the other side gives 1.h4xg3 e.p g2-g4 2. g4xf3 e.p. f2-f4 3.f4xe3 e.p, whereby the previous move by White has been e2-e4. However, this is an illegal position. The three missing white pieces were captured by black pawns. But R(h1) could not get out to be captured.
b) If White has made the captures e.p., then the retraction e5xd6 e.p. is not possible as the black king would have been in check. The attempted retraction 1.a5xb6 e.p. b7-b5 2.b5xc6 e.p c7-c5 3.c5xd6 e.p .leads to.an illegal position. The three missing black pieces have been captured by white pawns, but B(c8) could not escape to be captured.
Solution: The three consecutive e.p. captures have been made by the pawns a6, b6 and c6, giving unique retractions.
