Proof Games are a spinoff from Retros.  In a PG, the determination of previous moves goes all the way back to the starting position.  To solve, you must find the complete gamescore leading to the position in the stipulated number of moves.  In a sound PG, there will be only one gamescore possible, unless stated otherwise. 

"PG in 10.0 moves" means that the diagram will be reached after black's tenth move.  The number is always in full moves, as in helpmates.  Thus, "PG in 10.5 moves" implies the diagram is reached after white's 11th move.  The only constraint on the moves is legality; both sides move cooperatively to reach the diagram, no matter how bizarre the moves may be. 

1s1qksRr/2ppp1p1/b2r3p/1P3p2/6P1/8/1PPPPP1P/1SBQKBSR

A quick scan reveals the "problem piece" wRg8.  Clearly, it will take some clever maneuvering to get him there.

Solution:  Click & hold left mouse button and highlight the area below:

1.a4 b5 2.axb5 a6 3.Rxa6 f5 4.Rf6 The most logical entry point for wR, but how will the black King avoid contact? 4...Ra6 5.g4 Rd6 6.Bg2! A shield by another white piece, that's how! 6...Ba6 7.Bd5 Qc8 8.Bf7+ Kd8 9.Be8 h6 10.Rxf8 Sf6 11.Rg8 Sh7 12.Bf7+ Sf8 13.Bd5 Ke8 14.Bg2 Qd8 15.Bf1

rs1k1KsQ/ppp1b2q/2p1pp2/7p/P5b1/1r6/1P1PPP1P/RSB2B2

The white King has taken quite a walk up the board.  So how did he get past all those black pieces?

Solution:  Click & hold left mouse button and highlight the area below:

1.c4 h5 2.c5 Rh6 3.c6 dxc6 4.Qc2! Fastest way to h8-important, since white's time is limited. 4...Bh3 5.Qh7 Qd3 6.Qh8 Qh7 7.Kd1 Rg6! Setting up an "Indian"- a piece retreats, then another piece masks it and then moves away. The motivation, of course, is to allow wK to pass. 8.Kc2 Rxg2+ 9.Kc3 Rxg1 You might have noticed in the diagram that black's last move involves a Bishop capture on e7-how else to uncheck? White's Rh1 is the easiest piece to sacrifice. 10.Kd4 Rg4+ 11.Ke5 f6+ 12.Ke6 Kd8 13.Kf7 e6 14.a4 Ba3 15.Rg1 Rb4 The 2nd Indian (unmasking Bh3) 16.Rxg7 Bg4 17.Kf8 Rb3+ A third Indian. 18.Re7 Bxe7#

Michel Caillaud
2nd-4th Prize
StrateGems 2002
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PG in 20.5 moves  (16+16)

Q1Bk4/ppp2ppp/1sq3bs/2rpp1r1/4P3/2b5/PPPP1PPP/RSB1K1SR

Oddly enough, the third example also involves an infiltrating white piece!  It seems to be a good device for this genre.

Solution:  Click & hold left mouse button and highlight the area below:

1.Sc3 Already not obvious on move 1! The wS will get plenty of exercise. 1...e5 2.Sd5 Qf6 3.Se7 White's Queen must enter at e6 to avoid a collision with Black's Bc8. White has the foresight to screen bK. 3...d5 4.e4 Bf5 5.Qe2 Sd7 6.Qa6 Rd8 7.Qe6 Sb6 8.Qc8 Sh6 9.Sc6 Bb4 10.Qa8 Bc3 11.Sb8 Another screen unpins bR. 11...Rd6 12.Bb5+ Kd8 13.Bd7 Rc6 14.Bc8 Rc5 White's pieces are stuffed in the NW corner, but how does his S go back home? Amazingly, only one route works. 15.Sd7 Qc6 16.Sf6 Re8 17.Sg4 Re6 18.Se3 Rg6 19.Sc4 Rg5 20.Sa3 Bg6 21.Sb1!