Puzzle - White mates in two moves

I don't know the answer

I think it's Qe8.

Then it depends on what black does but I think white has mate in all continuations

1bd7 nkd7 2 rd5

Black takes the rook by Rxd5

Qe8 is clever as all black’s discovered checks are all met with mate, problem is it doesn’t actually threaten anything and black can move the B on b2. Must admit I stared at it for a couple of minutes and nothing really jumped out so I put it into Stockfish to satisfy my curiosity.

When solving a complex M2 composition like this one, look for strong black defences and see how White can deal with them. Here the strong defences are the discovered checks on the d-file, and white mating replies are already prepared for them, e.g. 1...Bc4+ 2.Bd7, 1...Be6+ 2.Bd3 – all double-check(mate)s. The most important set variations are 1...Bxf7+ 2.Bd3 – not 2.Bd7+? because of 2...Kg6!, and 1...Bxf3+ 2.Bd7 – not 2.Bd3+? because of 2...Kg4!

Since Black has many random moves that don't allow an immediate mate, White needs to find a first-move that generates a M1 threat. 1.Qg7? threatens 2.Qg4, then the checking defences on the d-file are answered as in the set play, while 1...Rd4 permits 2.Qxf6. However, Black refutes this with 1...Re2!, another strong defence that enables the black king to escape to e5. Likewise, 1.h8=Q? threatening 2.Qfh7/Qhh7 is defeated by 1...Re2!

How do we deal with 1...Re2? Promising is 1.Re4? which threatens 2.Ng3/Ng7, but the white rook has blocked the potential double-check 2.Bd3, and so Black refutes by 1...Bxf7+! which gives the king an escape on g6. 1.Re7/Re8? don't help as they don't generate a threat.

The correct key-move is the brilliant 1.Rg1! which surprisingly gives the king a flight-square on e5. The threat is 2.Rg5, against which 1...Re2? is now pointless. If 1...Ke5 (interfering with the b2-bishop), then 2.Qxf6. Most discovered checks on the d-file allow the double-check mating replies as in the set variations mentioned before. However – and this is the main theme of this composition – the white replies to the important defences 1...Bxf7+ and 1...Bxf3+ are now changed from the set play, thanks to the new placement of the key-rook which guards the g-file instead of the e-file. After 1...Bxf7+, only 2.Bd7 works – not 2.Bd3+? because of 2...Ke6!, and after 1...Bxf3+, only 2.Bd3 works – not 2.Bd7+? because of 2...Ke4! So compared with the set variations, White's mating replies to 1...Bxf7+ and 1...Bxf3+ are reciprocally changed.

This is a First Prize winning problem composed by the late Michael Lipton, a British problemist who passed away last year.