Shortest proof game

What was the shortest game, if:

a) White moved last.
b) Black moved last.

Let me try a). The final position has white pieces/pawn that require at least 9 moves. All white pieces captured are pawns. At least one of these pawns must have moved before being captured, to allow white to play his first moves, because black needs more than 2 moves to capture a pawn on it's original square. White has only 2 moves available wihtout pawn moves or capture, so, white made at least 10 moves. Like:

1.e4 (the pawn move) Nf6 2.Bb5 Nxc4 3.c4 Nxd2 4.Bxd2 h5 5.Ba5 Rh6 6.Kd2 Rg6 7.Kc3 Rxg2 8.Kb4 Rxh2 9.Nc3 Rh3 10.Rh3.

That is the correct solution of a). 🙂

b) looks more complicated. The last (black) move must have been a pawn move (h7-h5 or h6-h5). It could not have been the knight on c8 because the white could would be in check before the move. Hence, the rook has been captured by a white knight, either on h8 or on h7 (after h7-h6 and Rh8-h7). The capture on h7 has the advantage of being 'closer' to the knight from b1. Disadvantage is that black has to spend 2 tempi at the start of the game despite the need for an early capture of the d- or e-pawn. Therefor I looked at the alternative and used the other knight to do the trip back and forth to h8. This is what I have at the moment:

1.Nf3 Nf6 2.Nh4 Ne4 3.Ng6 Nxd2 4.Nxh8 Nb3 5.Bd2 Nd4 6.Ba5 Nxe2 7.Kd2 Nf4 8.Kc3 Nxg2 9.Kb4 Ne1 10.Bb5 Nf3 11.c4 Nxh2 12.Nc3 Nf1 13.Ng6 Ne3 14.Nh4 Ng2 15.Nf3 Nf4 16.Ng1 Nh3 17.Rxh3 h5.

Anyone has shorter and/or more fundamental explanation?

Originally posted by Mephisto2
b) looks more complicated. The last (black) move must have been a pawn move (h7-h5 or h6-h5). It could not have been the knight on c8 because the white could would be in check before the move. Hence, the rook has been captured by a white knight, either on h8 or on h7 (after h7-h6 and Rh8-h7). The capture on h7 has the advantage of being 'closer' to the kn ...[text shortened]... 2 15.Nf3 Nf4 16.Ng1 Nh3 17.Rxh3 h5.

Anyone has shorter and/or more fundamental explanation?

There is one other possibility for Black's last move: ...g6xh5! This saves three full moves.

1.g4 Nf6 2.g5 Ne4 3.g6 Nxd2 4.Bxd2 hxg6 5.Ba5 Rh5 6.Kd2 Re5 7.Kc3 Rxe2
8.Kb4 Re3 9.Bb5 Rf3 10.c4 Re3 11.Nc3 Rf3 12.h4 Rg3 13.h5 Rh3 14.Rxh3
gxh5

However, I don't much like that solution because at the end, Black's Rook is just killing time. Perhaps there is a way to save yet more moves.

Originally posted by BigDoggProblem
There is one other possibility for Black's last move: ...g6xh5! This saves three full moves.

1.g4 Nf6 2.g5 Ne4 3.g6 Nxd2 4.Bxd2 hxg6 5.Ba5 Rh5 6.Kd2 Re5 7.Kc3 Rxe2
8.Kb4 Re3 9.Bb5 Rf3 10.c4 Re3 11.Nc3 Rf3 12.h4 Rg3 13.h5 Rh3 14.Rxh3
gxh5

However, I don't much like that solution because at the end, Black's Rook is just killing time. Perhaps there is a way to save yet more moves.

Nicely done, much better than my solution. But you are right, there must be something else (or more), because your idea leads to multiple solutions, for instance

1.g4 Nf6 2.g5 Ne4 3.g6 Nxd2 4.h4 Ne4 5.Bd2 Ng3 6.Ba5 Nxe2 7.Kd2 Nf4 8.Bb5 hxg6 9.Kc3 Rh5 10.Kb4 Rd5 11.c4 Rd3 12.h5 Rc3 13.Nxc3 Nh3 14.Rxh3 gxh5

But you are right, there must be something else (or more), because your idea leads to multiple solutions, for instance

1.g4 Nf6 2.g5 Ne4 3.g6 Nxd2 4.h4 Ne4 5.Bd2 Ng3 6.Ba5 Nxe2 7.Kd2 Nf4 8.Bb5 hxg6 9.Kc3 Rh5 10.Kb4 Rd5 11.c4 Rd3 12.h5 Rc3 13.Nxc3 Nh3 14.Rxh3 gxh5

This is true. The correct solution is dual-free.

Finally got it. 13.0 moves, and an exact PG.

1.e3!!

Black's got the spare time, so White makes what is shockingly his most freeing pawn move.

1...h6!

And a great reply. One assumes the N must immediately start a rampage, but it's more important to keep White moving.

2.Bd3 Rh7 3.Bxh7 Nf6 4.Bd3 Ne4 5.Bb5 Nxd2 6.c4 Nf1 7.Bd2 Nxh2 8.Ba5 Ng4 9.Kd2 Nxe3 10.Kc3 Nxg2 11.Kb4 Nf4 12.Nc3 Nh3 13.Rxh3 h5

Originally posted by BigDoggProblem
Finally got it. 13.0 moves, and an exact PG.

1.e3!!

Black's got the spare time, so White makes what is shockingly his most freeing pawn move.

1...h6!

And a great reply. One assumes the N must immediately start a rampage, but it's more important to keep White moving.

2.Bd3 Rh7 3.Bxh7 Nf6 4.Bd3 Ne4 5.Bb5 Nxd2 6.c4 Nf1 7.Bd2 Nxh2 8.Ba5 Ng4 9.Kd2 Nxe3 10.Kc3 Nxg2 11.Kb4 Nf4 12.Nc3 Nh3 13.Rxh3 h5

Yes, that is the solution.

The problem is by Michel Caillaud, Probleemblad, Jan. 2000.
It shows a record in difference (3.5 moves) between the shortest proof game with white and the shortest proof game with black to move, where both proof games are dual-free.