Problem 55 is an elegant example of a changed half-pin.  Set mates are provided for all of Black’s moves.

1…Sd-any – self-pinning the b6-knight – 2.Qd5.

The other knight’s moves, besides completing the half-pin, demonstrate correction play.  A ‘random’ move such as 1…Sa4 unguards c8 and permits 2.Qc8.

The knight ‘corrects’ this error by 1…Sd7!? which, however, contains a new error (self-block), allowing 2.Qg8.

The key 1.Qc7! creates another block position and changes two of the set mates.  1…Sd-any 2.d5, 1…Sb-random 2.Qc8, 1…Sd7!? 2.Qc4.

One reason for the half-pin’s popularity is its capacity for blending with other themes.

Problem 56 features four half-pin defences that are answered by different battery mates.

1.Bg4! has the threat of 2.Rf3, which induces the d4-rook and b6-queen to move from the diagonal line, leaving the other pinned. 1…Rd3 2.cxd3, 1…Qb3 2.cxb3, 1…Rxg4 2.c4 (not 2.c3+? Kf3), and 1…Rf4 2.c3 (not 2.c4+? Bb2).

The battery mates are all fired by a white pawn, which on its initial square makes each of its four possible moves in turn – this is the Albino theme.

There is by-play, 1…Qc6/b7 2.Bxd4.

The half-pin theme is tripled in Problem 57.

Three complete half-pins are the highest number to have been achieved in a two-mover, making this an example of a task problem – a work that attains a maximum effect.

The sacrificial key 1.Qe2! threatens 2.Qxf3.  The three pairs of main variations are:

     1…Rf6 2.Sg5, 1…Rf5 2.Sd6;
     1…Sd4 2.Qxe3, 1…Sxc3 2.Qxc4;

     1…Bxe2 Sxc5, 1…Bxc3 2.Qd3.

That each half-pin line utilises two black pieces of the same type adds further to the unity of this composition.

Finally, 1…fxe2 allows 2.f3.

The helpmate 58 illustrates an anticipatory half-pin.  That means the half-pin set-up arises only during the course of play, instead of being fully formed in the initial position.

Part (a) of this twin is solved by 1.Bb8 Rc6+ 2.Kb5 c4, and

...part (b) by 1.Bg8 Bc6 2.Kc5 Bf2.

The first bishop move in each solution unpins a white piece and also prepares for the other black bishop to be pinned on the fifth rank.  Then a white Grimshaw interference on c6 enables the black king to move onto the pin line.

A white half-pin arrangement in helpmates typically yields the following play: White moves away one of the two pieces on the thematic line, leaving the other pinned, then Black interposes a piece on the line, freeing that second white piece to deliver mate.

The solutions here are (a) 1.Bh6 Rg8 2.Rdf3 Sf6, and

(b) 1.Qg8 Sf4 2.Rd5 Rh2.

Each part culminates in a double pin-mate, in that the mating position requires two black pieces to be pinned in order to be effective.

Also, every pair of half-pinned pieces exchange their functions across the two solutions.  For example, with the white pair, in (a) the rook guards flights and the knight mates, while in (b) the knight guards a flight and the rook mates.