Found while looking for something else...

[alexpgp]

In chess, a helpmate is a chess problem in which both sides cooperate in achieving the goal of checkmating Black. A duplex helpmate is a helpmate with two solutions (one where Black moves first and helps White mate Black, and the second, where White moves first and helps Black mate White).

I was digging around one of the bottom shelves in my office and ran across a folder of old papers, and among them was a duplex helpmate in two moves—a poor thing, but mine own—that I had devised back in college. This is the position:



The solutions are:

(a) 1...Bc8 2. Rxf7 Re8 3. c7 mate (but see the notes below)

and

(b) 1. Ra1 Bxc6 2. Rg1 Rh4 mate.


Cheers...

Notes: In his comment, paladin3 indirectly points to there being multiple solutions for (a) here, in which Black need only make indifferent moves with the Rook or pawn, e.g., 1...f6 2. cxb7 f5 3. b8=Q mate, or by removing the Bishop to a8, e.g., 1...Ba8 2. c7+ Ke8 3. c8=Q mate.

There is no obvious fix.

(1) Add a Rook on a8? 1...f6 2. cxb7 f5 3. cxa8=Q mate.

(2) Add a Rook on b8? 1...Ba8 2. c7+ Ke8 3. cxb8=Q mate.

(3) Add a Knight on b6? 1...Nc4 2. cxb7 f5 3. b8=Q mate.

(4) Add a Knight on b6 and a Rook on b8? ...

Comments

[paladin3.livejournal.com]

I saw the black helps white right off - but I did (anymove by bishop out of the way), P-B7, Check, K to Q1, P-B8, Queened, Checkmate

The white one does not make sense. Can't the king just move to Kn1 and be out of the way of the rook and the Bishop? Apologies for reader density and sloppy chess notations...

[paladin3.livejournal.com]

oh wait...I'm not used to the A1 notation system...you mean you move the rook to the White's QKn1 blocking the king's escape....sorry

[alexpgp.livejournal.com]

No problem.

Looking at your solution, it would appear there are two solutions to the "Black to move and helpmate in two," the second one being:

1...Ba8 (no other move will do, as ...Ba6 defends the queening square) 2. c7+ Ke1 3. c8=Q mate (1...B-R1 2. P-B7 ch K-K1 3. P-B8=Q mate).

Hmmm, it occurs to me there's also a third solution, in which Black wastes time with his pawn or Rook, whereupon White takes the Bishop with the pawn and then queens.

Off the top of my head, I'm thinking that a second Black Rook on b8 (no, that won't do... how about a8?) might reduce the number of solutions back down to one. No, that won't do, either. This composition will require more thought.

In the "White to move and helpmate in two," White's second move with the Rook is from a1, in the corner, to g1, up against his King. So when the Black Rook moves to h4 (Black's R5), White's King is in double check and is mated.

Cheers...