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...