It’s Black to move. What must Black do in order to help White castle queenside in just 11 moves?

• It seems like there are quite a lot of ways to do this. Is there some extra clever thing going on here that no one has spotted yet? – Gareth McCaughan Oct 17 '19 at 23:36
• "In just 11 moves" does indeed narrow it down further. – Gareth McCaughan Oct 17 '19 at 23:38

This seems to work

1. -, Kg1
2. h5, Bg2
3. h6, Bf1
4. h4, Be2
5. h5, Bd1
6. h3, Be3
7. h4, Rc1
8. a5, Rc4
9. a6, Bb3
10. axb3, b2=N
11. bxc4, Nd2
12. O-O-O, -

• A neater approach, I think, than mine. Mine was a bit "brute force". Interesting that it's the same length. – Dr Xorile Oct 18 '19 at 1:13
• Thanks, but you showed there isn't a unique solution. :) – Jens Oct 18 '19 at 1:21

Here's an answer. It's 11 moves by black and by white. Same length as @Jens:

1... Kg1 2. e5 Bg2 3. h5 Bxh3 4. h6 Bd7 5. e6 Kg2 6. exd7 Kg1 7. d8=Q Kg2 8. Qd1 Kg1 9. Qxc1 Kg2 10. Qxb1 Kg1 11. Qxb2 Kh1 12. O-O-O#

• That seems to be only $11$ moves for white, like my solution? – Jens Oct 18 '19 at 1:07
• Oh, yes. I can't count. LOL. Yes, so the same length as your solution! Although a totally different approach. – Dr Xorile Oct 18 '19 at 1:10

One way is:

1... Kg1
2. d5 Bg2
3. h5 Bf1
4. d6 Be2
5. h6 Bd1
6. h4 Be3
7. h5 Bb6
8. h3 Bc7
9. dxc7 d6
10. c8=Q d5
11. Qa6 d4
12. Qxa3 d3
13. Qxb2 Rxb2
14. a3 Bb3
15. a4 Bg8
16. O-O-O

After

1. ... Kxh2 White has six pawn moves before they have to move their King. Black can then play Bg2-f1-d3-g6 (somewhere in the line, White can play e5) so that White can play hxg6 and promote their pawn.

From there, I believe Black can essentially waste their turns playing Kh1-h2/g1 ad infinitum while White cleans up the left side of the board and eventually plays O-O-O.