So in the set play, if Black plays 1…Rb7, then 2.Rc6, and if 1…Bb7, then 2.Re7.  Another Grimshaw occurs on g7, 1…Bg7 2.Qxf7 and 1…Rg7 2.Qe5.  These mutual obstructions between a rook and a bishop are called Rook-Grimshaws.

The less common Pawn-Grimshaw, in which a pawn and a bishop hinder each other, is also illustrated in this problem, with 1…f6 2.Qe4 and 1…Bf6 2.Qg4 completing the principal variations.

Note how a Pawn-Grimshaw is possible only when the pawn is on its initial rank, where its double-step can be disrupted.

As arranged in the diagram, 1…Rc3 allows 2.Se5, and 1…Bc3 allows 2.Se3.  White has a try, 1.Sf2?, which controls d3 and threatens 2.Qb4.

This try move abandons the set knight mates, but the added guard on d3 enables White to substitute the queen as the mating piece against the same defences: 1…Rc3 2.Qf4 and 1…Bc3 2.Qd3.  The try is defeated by 1…Rb3!, however.

The key 1.Be3! attacks c5 and threatens 2.Rb4.  The set mates are disabled again, but since the key-piece controls d4 as well, the white queen is able to take advantage of the interferences in yet another way, 1…Rc3 2.Qd4 and 1…Bc3 Qe2.

Initially, a knight mate on f7 is stopped only by the pin on the long diagonal, so unpinning the knight as the first move seems plausible.

The try 1.Rc3? does this, but hampers the bishop mate on b4, and so permits Black to escape with 1…Bc6! (a move which answers the threat of 2.Sf7 by removing the b5-bishop’s guard of d7).

1.Bc3? reciprocates the interference, impeding the rook mate on d3, so that Black can refute with 1…c6!  Therefore, we see a pair of white Grimshaw tries defeated by a pair of black Grimshaw defences.

The correct way to free the knight is 1.Ka2!, after which the defences on c6 are answered by the unobstructed rook and bishop mates, as in the set play.

One additional variation is 1…Bxe5 2.fxe5.

The helpmate 40 is constructed ideally in that every piece participates in the thematic play directly, with no extra pieces needed solely to prevent cooks.

In the two solutions, Black carries out a double Grimshaw to help White set up the sideboard model mates.

1.Bf5 Qd7 2.Rd6 Rb8, and 1.Bd6 Rg5 2.Rf5 Qh5.

Notice how Black’s moves are all unified in their effects – in every instance, Black not only closes a black line of defence, but also opens a line for a white piece to travel through.

In Problem 41, a black Grimshaw occurs as part of a more elaborate manoeuvre.

In the first solution, the e4-bishop wants to unguard e4 to allow Re2 mate, and the e6-rook wants to be moved to enable the white bishop to control the f5-flight.

To accomplish both tasks in time, Black plays the bishop over a critical square, g6, which the rook then occupies for an interference: 1.Bh7 Bd8 2.Rg6 Re2.

In the second solution, the e6-rook must unguard d6 for Bc7 mate, and the e4-bishop must move to let d4 be guarded by the white rook.  Again, only a critical move followed by an interference are capable of achieving both ends: 1.Rh6 Rf2 2.Bg6 Bc7.