# Overlap two Chess Games

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

The following rule will be considered.

• 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).

### Example of a solution with 45 moves

#### Game A, 20 moves

1. d4 d5 2. e4 dxe4 3. Bd3 exd3 4. Qh5 Nf6 5. Qxf7+ Kxf7 6. Nf3 Ng4 7. Ne5+ Ke6 8. Bh6 gxh6 9. f3 Nf2 10. Kxf2 Nc6 11. cxd3 Qxd4+ 12. Kg3 Na5 13. Nf7 Kxf7 14. b4 Qxb4 15. f4 Qxf4+ 16. Kxf4 c5 17. Nc3 Bh3 18. Nb5 Rc8 19. Nxa7 Nb3 20. Nxc8 Na5


#### Game B, 25 moves

1. a4 a5 2. Ra3 Na6 3. h4 h5 4. Nf3 f5 5. d4 b5 6. g4 Bb7 7. Bg2 c5 8. b4 Qb6 9. dxc5 Qxc5 10. Qd6 Qxf2+ 11. Kd2 Bxf3 12. Qxa6 Qxh4 13. Qxa8+ Kf7 14. Bxf3 Qxh1 15. Bb2 axb4 16. axb5 Nf6 17. gxf5 g5 18. fxg6+ Kxg6 19. Qxf8 Qxb1 20. Qxf6+ Kh7 21. Bxh5 Qxb2 22. Rb3 Qxb3 23. cxb3 exf6 24. Bg6+ Kxg6 25. e4 Rg8


#### Merged valid game (A and B overlapped)

• The kings could instead be required to occupy the same positions in both games. An interesting challenge either way. Commented Aug 12 at 16:05
• When you say the overlap must be a valid chess position, does it have to be reachable from the start position with normal play?
– xnor
Commented Aug 12 at 22:26
• @xnor, yes this is what is intended :)
– JKHA
Commented Aug 12 at 22:38

This seems closely related to the two king task. The optimal solution by G.Ponzetto

Game 1:

1.e2-e4 d7-d5 2.e4xd5 Qd8xd5 3.Bf1-d3 Qd5xa2 4.Bd3xh7 Qa2xb1 5.Bh7xg8 Qb1xc2 6.Bg8xf7+ Ke8xf7 7.Ra1xa7 Qc2xc1 8.Ra7xb7 Rh8xh2 9.Rb7xb8 Rh2xg2 10.Qd1xc1 Rg2xg1+ 11.Rh1xg1 Ra8xb8 12.Qc1xc7 Rb8xb2 13.Qc7xc8 Rb2xd2 14.Qc8xf8+ Kf7xf8 15.Rg1xg7 Rd2xf2 16.Rg7xe7 Kf8xe7 17.Ke1xf2

together with a trivial

Game 2:

1.f2-f4

should be pretty hard to beat.

Total number of half moves: 34

• It's also fairly clear that 33 half moves is a lower bound. (Since the first two half moves of any game cannot be captures, it is never optimal to capture pieces in both games.) This bound can only be achieved if we are able to find a 16.5 move game A in which the bK does not move at all (needs to be bK, since wK necessarily has the last move and cannot capture on his home square without wasting time). I have not been able to construct such a game but it may well be possible Commented Aug 13 at 8:14
• rot13("Gurer pna'g or n cvrpr ba n fdhner ba tnzr O vs gurer vf nyfb n cvrpr ba guvf fnzr fdhner va tnzr N, naq ivpr-irefn." Gurer vf n oynpx cnja ba r7 va Tnzr N naq n oynpx xvat ba r7 va tnzr O. Qba'g xabj vs vg pbhagf nf bireync gubhtu: "Gur bireynccrq tnzr jvyy bayl pbafvqre Juvgr xvat bs tnzr N naq Oynpx xvat bs tnzr O (gb cerirag univat 4 xvatf).") Commented Aug 13 at 22:33
• @Lucenaposition If it was meant that way, fixing it (at the cost of one half move) is easy enough. Commented Aug 13 at 23:39
• @TimSeifert Nor has the great Sam Lloyd... Commented Aug 13 at 23:42

Here's my silly attempt:

Game A:

1. e4 h5 2. Qxh5 d5 3. Qxd5 Rxh2 4. Qxb7 Rxh1 5. Qxc8 Rxg1 6. Qxb8 Rxg2 7. Qxa8 Rxf2 8. Qxa7 Rxd2 9. Qxc7 Rxc2 10. Qg3 Rxb2 11. Qxg7 Rxa2 12. Qxg8 Kd7 13. Qxf7 Rxa1 14. Qxf8 Rxb1 15. Qxd8+ Ke6 16. e5 Kxe5 17. Bc4 Rxc1+ 18. Ke2 Rxc4 19. Qxe7+ Kd5 20. Qe4+ Kc5 21. Qxc4+ Kxc4

Final position in Game A:

Game B:

1. e3

Combining these two positions will then yield the Maximum Synergy Bongcloud:

which is (always) a legal position. (White will need to know some basic geometric shapes to reach this position with black to move, though.)

Game A can very likely be improved, and in any case a variation can probably be found such that Game B can be made even shorter.

First board:

1. e3 f6 2. f3 g6

Second board:

1.d3 d6 2. Bg5 Bg4 3. Bxe7 Bxe2 4. Bxd6 Bxf1 5. Bxc7 Qxd3 6. Bxb8 Qxc2 7. Bxa7 Rxa7 8. Qxc2 Rxa2 9. Qxh7 Rxb2 10. Qxg8 Rxb1 11. Rxb1 Rxh2 12. Rxb7 Rxh1 13. Rxf7 Rxg1 14. Rxg7 Rxg2 15. Qxf8+ Kxf8 16. Kxf1 Rxf2+ 17. Kxf2 Kxg7

Combined board