A variant of the 2-Chess Games overlapped

Question

This is a variant of this previous puzzle.

Create two valid Chess games (A and B) with the minimum number of moves such that overlapping the two games creates a valid chess position.

The following rules will be considered.

Games A and B must have the exact same number of moves.
There can't be a piece on a square on game B if there is also a piece on this same square in game A, and vice-versa.
The overlapped game will only consider White king of game A and Black king of game B (to prevent having 4 kings).

Let me type some words, to see if i understood the situation. There are regular moves of two chess games, $A,B$, having the same number $N$ of half-moves, they may be not ended. After these $N$ half-moves we take a new chess board $C$ and teleport all pieces from the boards $A,B$ to their final positions, except for the black $A$-king, and the white $B$-king. There are no collisions of two pieces landing on the same square. This position must be regular, achievable from a normal chess game. Is it so? Well, it may be hard to prove minimality... — dan_fulea, Commented Aug 15 at 12:46
I would suggest to be consistent with using the term "game" for a sequence of moves and "position" for a board state. I was also confused by the meaning of "overlapping the two games": i thought it meant interleaving the moves of the two games! — wimi, Commented Aug 17 at 11:11
Trivial lower bound is 8.5 moves on each board. Because we need 30 total captures which requires at least 7.5 moves on each board. And the first 1.0 moves no one can capture. — Benjamin Wang, Commented Aug 17 at 17:04
@BenjaminWang Trivial lower bound is 9 moves on each board, as black must make 8 captures in one game. — Daniel Mathias, Commented Aug 17 at 21:03

Albert.Lang · Accepted Answer · 2024-08-17 14:51:38Z

2

Note: I assume the discarded kings to be exempt from the no-collision rule.

Game 1:

1. d4 h6 2. Bxh6 e5 3. Na3 Bxa3 4. Bxg7 Nf6 5. Bxh8 Bxb2 6. Bxf6 Bxa1 7. Bxe5 Bxd4 8. Bxc7 b6 9. Bxb6 Bxf2+ 10. Bxf2 Qb6 11. Bxb6 axb6

Game 2:

1. e4 Na6 2. Bxa6 d5 3. h3 Bxh3 4. Bxb7 Bxg2 5. Bxa8 Bxh1 6. Bxd5 Bxe4 7. Nf3 Bxf3 8. Qe2 Qxd5 9. Qxf3 Qxa2 10. Qxf7+ Qxf7 11. c4 Qxc4

I do not claim minimality.

Overlay Game 2 pieces circled:

answered Aug 17 at 7:33

Albert.Lang

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$\begingroup$ Can you post the moves and position of the final overlapped game for completeness? I suppose it'd be 1. Nf3 b6 2. Ng1 Ba6 3. Nf3 Qc8 4. Ng1 Qb7 5. Nf3 Qc6 6. Ng1 Bc8 7. Nf3 Qc4 8. Ng1 $\endgroup$
– justhalf
Commented Aug 17 at 14:08
$\begingroup$ @justhalf I don't see the point in a proof game as it is fairly obvious the position is reachable, but I've added an overlay. $\endgroup$
– Albert.Lang
Commented Aug 17 at 14:53
$\begingroup$ I mean, the proof game is short.. and I already typed it =p $\endgroup$
– justhalf
Commented Aug 17 at 15:07

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