# The Dropper, But With A Twist

Here's a piece-drop puzzle of my own.

In the below position, a White piece is to be dropped onto the board. This means that, before White can move, they must legally put a single piece on them board.

However, there is a special requirement that must be fulfilled by the piece drop.

The Requirement:

A single White piece has to be legally placed on the board such White can checkmate Black in precisely 12 moves. Additionally, there must be only one possible way to complete the checkmating sequence. Or, in a chess problemist's terms, it must be dual-free.

You must justify your choice of "droppage". by providing the mate in 12 sequence and explaining why it is a unique solution.

I accept any alternative answers that I have not thought of.

Have fun solving everyone!

This might be wrong because I haven't checked it with a computer.

Let's assume black wouldn't move at all. Then we would have a mate in 11 moves by walking with the king to f7 (capturing the black pawn) then to g8 and then queening the f6 pawn and mating the black king. But there are 2 problems: we need to mate in 12 moves, and black will of course move.

We can effectively prevent black from moving by placing a bishop on a7. If black would move any of the pawns he would get mated by the bishop. Only thing black can do is to shuffle his bishop. This leaves us with the one move we have to loose. This can be achieved by placing the bishop on b8 and then moving it in the first move to a7, then we mate as described at the beginning in 11 more moves. Therefore the solution is placing the bishop at b8 and the following sequence of moves:

1.Ba7 Ba2 2.Kg2 Bb1 3.Kf3 Ba2 4.Ke4 Bb1 5.Kd5 Ba2 6.Kc6 Bb1 7.Kd7 Ba2 8.Ke7 Bb1 9.Kxf7 Ba2 10.Kg8 Bb1 11.f7 Ba2 12.f8=Q# (or f8=B#)

What's left is to show, why we can't keep the bishop at b8 and mate in 11 moves. This doesn't work because of the following sequence:

1.Kg2 b5 2.Kf3 Nb6 3.Bxc7 Nd7 4.Bd6 (otherwise black will capture the white pawn) Ba2

... and white will need at least 13 moves to mate.

• The, uh, queening of the White pawn was only something that I realized after the posting, but eh well. Commented Aug 19, 2019 at 16:25
• @RewanDemontay Well, the engine on my phone found a mate in 11 moves (and also one with 12 moves after 1.Kg2): 1. Ba7 Ba2 2. Kg2 Bb1 3. Kf2 Ba2 4. Ke1 Bb1 5. Kd2 Ba2 6. Nd3 c1=Q+ 7. Kxc1 Bb1 8. Kxb1 Nc2 9. Ne5 Na3+ 10. bxa3 b2 11. Nxf7# Is there actually a solution for 12 moves? Commented Aug 19, 2019 at 17:41
• +1 Gah...I had been stuck using a white white-bishop. Commented Aug 19, 2019 at 18:47

drop bishop to c6 and Bxa8, which black could only follow with b5, c6, c7 or Ba2. Which are all inconsequential except c6 which would allow white to mate in one less move. Assuming black's playing fair, it won't. That leaves White's King to wander about the board and capture Kxf7 followed by Kg8 and then Pawn promotes to either Bishop or Queen at f8 to check and mate black on its 12th move.

Explanation:

White's white bishop allows you to capture black's knight immediately while forcing white's king into play. White's Bishop cannot deliver checkmate singlehandedly (or with pawn or promoted pawn), it requires King's assistance, so even if you move Bishop to capture black's pawn at f6 you still need white's king to move all the way around the board and keep black's king from taking that pawn, while also increasing the number of moves. Meanwhile black only has inconsequential moves (exception stated above).

I don't know how to add a chess board highlighting the key moves.

• Unfortunately, that would not work-Black will start to pushing their pawns and they will soon break their pieces free of their prison and win. But you have identified the right piece. Commented Aug 18, 2019 at 13:10
• @RewanDemontay Yeah, I see it now. Rookie mistake. Commented Aug 18, 2019 at 14:29
• Don't really enjoy putting wrong answers. :-) Commented Aug 18, 2019 at 14:54
• @RewanDemontay I don't see how this could work with a bishop. If I place it at c6 black plays b5 and Nb6 and I will need at least 13 moves, because the knight now blocks the shortest route to c6. If I move the bishop or place it somewhere else, one of the black pawns queens. Commented Aug 19, 2019 at 14:43
• No, I say keep position. I'm quite happy like this. Been trying to figure this out has been fun and instructive. Commented Aug 19, 2019 at 15:37