2

Is 21 moves the least needed to get board down to 2 kings?

[FEN ""] 
1. e4 d5 exd5 Qxd5 Qh5 Qxa2 Qxh7 Qxa1 Qxh8 Qxb1 Qxg8 Qxb2 Qxg7 Qxc2 Qxf8 Kd7 Qxf7 Qxc1 Ke2 Qxd2 Kf3 Qxf2 Ke4 Qxf1 Qxe7 Kc6 Qxc7 Kb5 Qxc8 Qxg1 Qxb8 Qxh1 Qxa8 Qxh2 Qxa7 Qxg2 Kd4 Qd5 Kxd5 b6 Qxb6 Kxb6
13

Samuel Loyd found faster in 1895.

[FEN ""]
1. c4 d5 2. cxd5 Qxd5 3. Qc2 Qxg2 4. Qxc7 Qxg1 5. Qxb7 Qxh2 6. Qxb8 Qe5 7. Qxc8+ Rxc8 8. Rxh7 Qxb2 9. Rxh8 Qxa2 10. Rxg8 Qxd2+ 11. Kxd2 Rxc1 12. Rxg7 Rxb1 13. Rxf7 Rxf1 14. Rxf8+ Kxf8 15. Rxa7 Rxf2 16. Rxe7 Rxe2+ 17. Kxe2 Kxe7

https://pdb.dieschwalbe.de/search.jsp?expression=PROBID=%27P0001931%27

This is 17.0 moves.

It is also possible to do it in 16.5 moves but I can't find it yet. See Fran├žois Labelle's page.

3

I found the solution to the 16.5 massacre proof game that Remellion mentioned that Francois Labelle had found using a computer search! Well to be more accurate, I found a computer program that found the solution. But it is amazing nonetheless!

I discovered the Jacobi Fairy Chess Helpgame solver, made by Francois Labelle himself. Here is the code that you can use yourself to find all 25 possible games that end on this position: stipulation dia16.5 forsyth 8/5k2/8/8/8/8/5K2/8. It does take around 15 minutes to complete, however.

Here is one of the many solutions.

[FEN ""]

1. e4 d5 2. exd5 Qxd5 3. Bd3 Qxa2 4. Bxh7 Qxb2 5. Rxa7 Qxc1 6. Rxb7 Qxb1 7. Qxb1  Rxh7 8. Rxc7 Rxh2 9. Qxb8 Rxg2 10. Rxe7+ Kxe7 11. Qxc8 Rxg1+ 12. Rxg1 Rxc8 13. Rxg7 Rxc2 14. Rxg8 Rxd2 15. Rxf8 Rxf2 16. Rxf7+ Kxf7 17. Kxf2
2

No, that is not the quickest way.

The problem is that you have too many checks. The solution I came up with is to switch to using the rooks to eat pieces. This allows the board to be cleared in 18 moves:

[FEN ""]

1.e4 d5 2.exd5 Qxd5 3.Qh5 Qxa2 4.Qxh7 Qxb2 5.Qxg7 Qxb1 6.Qxg8 Rxg8 7.Rxb1 Rxg2 8.Rxb7 Rxf2 9.Rxc7 Rxd2 10.Rxa7 Rxc2 11.Rxa8 Rxh2 12.Rxb8 Rxh1 13.Rxc8+ Kd7 14.Rxf8 Rxg1 15.Rxf7 Rxf1+ 16.Kd2 Rxc1 17.Rxe7+ Kxe7 18.Kxc1  *

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