***SPOILER ALERT***
OK, I will start to explain the method I used. Anyone still working on it should avoid scrolling down.
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[This explanation is best suited for experienced PG solvers.]
Normally, to solve a Proof Game, we count the minimum moves needed for each side to reach the diagram position. However, in a PG like this, that approach is not very helpful. White has nothing on the board to even count!
Sound proof games [those with only the solution(s) intended by the composer, and NONE other] contain evidence as to what happened. In a problem like this, the absence of certain units is the key evidence. All of White's back-rank pieces, save the King of course, are missing. In particular, Bc1 and Bf1 are missing. Those two tell us much more about the game than the other missing pieces, because the pawn structure dictates that they never moved. Therefore, Black must have captured both of them at home.
At this point, it is easy for the solver to become overwhelmed. Not only do we have to clean out White's entire back rank, but Black has several pieces that need to be developed, and Pa7 and h7 are missing! Clearly, we need a way to focus our efforts. The last thing we want is to end up solving mainly by trial and error. This is how computers do it; they are much faster at it than we are, yet this problem is (currently) unsolvable by a computer!
The method I hit upon is this.
1) Concentrate on the most cumbersome sub-task you can find. Ignore other tasks.
2) Consider a scheme to accomplish that task [and try to use words, not moves, to describe the scheme].
3) Consider the sequence of the scheme you chose. Count only moves that directly pertain to that scheme. Count the same way that chess notation works. If White moves, then Black, count that as the same move number. If Black moves, then White, increment the count. Execute the scheme as fast as you possibly can. Ignore 'waiting' moves or moves to attain other plans. The idea here is to see if the scheme can be executed fast enough to satisfy the stipulation.
My, that was a lot of mumbo-jumbo. Hopefully, an example from the PG 21.0 will make it clearer.
1) Sub task: kill the two White Bishops. [Obviously this will take ages no matter how it is done.]
2) Scheme: kill both of them with Black's original Q [from d8].
3) Sequence: 1.a4 d5 2...Qd6 3...Qa3 [skip White moves that do not help the scheme, and don't worry about the exact route of bQ. We're more worried about speed right now.] 4...Qa1 [again, who cares whether we take the Rook or not. Focus on the Bishops!!] 5.N~ [The N gets out of the way; who cares where] 5...Qxc1 6...Qa1 7...Qa5 8.Qa1 [Now the ball is in White's court and we'll ignore most of Black's moves.] 9.Kd1 10.Kc1 11.Kb1 Ba3 [or the Q moves off the a-file and back, which is just as fast] 12.Ka2 Bc5+ 13.Kb3 Qa1 14...Qxf1 [scheme is done, but let's count the wK going back home, to make sure he can get there on time] 15...Qa1 16...Qa5 17...Ba3 18.Ka2 19.Kb1 20.Kc1 21.Kd1 22.Ke1. Bust! We're one move too slow.
It's fairly obvious that this scheme cannot be done faster. The hard part now is giving up on it. It's tough to abandon a scheme when it seems like it's so close to working, but [I hope] this sequence analysis shows conclusively that it cannot work.
Suggested next scheme: promoted Q kills c1, Qd8 kills f1. Anyone care to try it?
Extremely difficult PG
01 May '08 11:57
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