Sam Loyd, puzzle king

The first thing you do in a "mate in two" problem, is the examine the "set" play. This means you pretend it is Black to move first, and you find checkmate moves for White

Set Play:

1. ... d5 2. Sc5#

1. ... b2, Sb4/a3/e3/e1 2. Q(x)b4#

1. ... Ra3/b2 2. S(x)b2#

In this problem, every legal black move has a White mate provided in the initial position. Such a position is called a "block". Sometimes, to preserve the character of a block problem, you try to find a quiet White move, that keeps Black in this trouble. Can we do that here? Let us see. If Bd1 moves, Black can now play b2, and there is no pin on the knight(S) at c2, no mate Qb4. If Bxc2, Sxc2. Strong checking moves by the Queen are useless, since 1.Qa7ch? Kb5 and the king escapes. The White rook cannot move gainfully. It releases the e-pawn 1...e5+ by Black would not be nice. How do we find a quiet move?

Some more terminology for future use. Neither the Black p at b3 nor S at c2 are pinned, but they can be said to be half-pinned. A great English composer Comins Mansfield, made many problems where the main line of play uses halfpins. Entire books have been written about problems with half-pins "Het Half-pin thema" in Dutch.

Have you solved it yet?

Sam Loyd was one tricky guy. The key move does not preserve the quiet. It introduces a threat. Such problems with a block in the set play and a threat in the "key" (the solution's first move) are called "block-threat" problems and are both rare and difficult to solve. Here the key is 1.Sa3! (>2. Threat Qa7#) (By covering b5, the threat is set up for the mate.) Here are the variations

1. ... Kxa3 2. Qa5/a7#

1. ... b2, Sb4/xa3 2. Q(x)b4#

1. ... Rxa3 2. Sb2#