All chess moves involve two basic effects: the departure from a square, and the arrival on a square.  These concrete effects of a move underlie most of what problemists would call strategic play, such as the firing of a battery (a piece’s departure from a square opens a line of attack), and self-interference (a piece’s arrival on a square closes a line of defence).

Strategy in this problem sense also includes, besides the various forms of line play, some motifs that specifically relate to squares.  The main examples of the latter are (1) square-vacation, in which a piece’s departure from a square enables a friendly piece to occupy it, and (2) square-obstruction, in which a piece’s arrival on a square prevents a friendly piece from occupying it.

Let us examine some compositions that make use of such motifs thematically, i.e. repeat them in a pleasing way.

This problem is in fact a mutate, with set mates provided for all of Black’s moves in the diagram; two of these set variations have been changed by the key: 1…dxc6 2.Rd7, and 1…Nxc6 2.Rxd7.  Self-blocks are the only type of black square-obstruction that can be rendered in a two-mover, because of the short play.

In the more-mover 116, White seeks to give a battery mate on the h-file by moving the rook to an un-guarded square, but careless attempts to do so would fail due to the harassing black knights, e.g. 1.Rh3? Ng5! 2.Rh4 Ng6, or 1.Rh4? Ng6! 2.Rh5 Nh4/Ng5.

To mate in four moves, White must manipulate the black pawn into obstructing the squares needed by the knights.

1.Rh5! g6 2.Rh4 – now correct since 2…Ng6 is no longer an option – 2…g5 3.Rh3 – similarly playable now that 3…Ng5 is precluded – 3…g4 4.Nxg4.

116. Hilding Fröberg & Gustav Hultberg
Eskilstuna Kuriren 1942

Mate in 4

Problem 117 shows square-obstruction by both White and Black.
 

White has two natural ways to start, 1.Bd8 to threaten 2.Bxf6, and 1.Nd8 to threaten 2.Nf7.  Black’s only defences to these moves are, respectively, 1…Nd5 to cover f6, and 1…Bd5 to cover f7.  Both of these defences occur on d5, so the two black pieces will hinder each other when either plays to that square.

However, after 1.Bd8? Nd5!, White cannot exploit the disabling of …Bd5, because the try move itself has blocked a vital square, ruling out the continuation 2.Nd8.

Similarly, 1.Nd8? is refuted by 1…Bd5!, when White cannot proceed with 2.Bd8 to take advantage of Black’s inability to play …Nd5.

Therefore we have, for each player, a mutual obstruction between bishop and knight.

117. Siegfried Brehmer
Die Schwalbe 1950
German Ring Tourney, 5th Prize

Mate in 3

The solution is 1.Rg6!, which threatens 2.Rxf6 and 3.Rf8.  The thematic defences work against the threat, but now their obstruction errors are exploited: 1…Bd5 2.Bd8 and 3.Bxf6, and 1…Nd5 2.Nd8 and 3.Nf7.
 

Problem 118 features multiple instances of square-vacation, coupled with queen sacrifices.

The key 1.Nb6! aims to mate on d5 after that square has been vacated by the queen.  White is required to give a forcing queen check on the second move, one that also doesn’t allow Black to reply with either a check or a guard on d5.

Initially only one such queen move qualifies, making it the threat: 2.Qe5+ Nxe5 3.Nd5.  Any move by the black rook would defend by opening the long diagonal for the bishop – 2.Qe5+? Bxe5+!, and depending on where the rook goes, four more square-vacating sacrifices follow.

A ‘random’ rook move that relinquishes control of d2, such as 1…Rb3, permits 2.Qd2+ Nxd2 3.Nd5.

118. Alexander Kuzovkov
Thémes-64 1985
1st Prize

Mate in 3

Black ‘corrects’ the error of un-guarding d2 by moving the rook on the rank, but new errors arise when the rook interferes with the other black bishop or the queen, 1…Rc2 2.Qe4+ fxe4 3.Nd5, 1…Re2 2.Qd3+ Bxd3 3.Nd5, and 1…Rf2 2.Qxf3+ Rxf3 3.Nd5.

Two secondary variations are 1…Qxe1 2.Qxf3+ Kd2 3.Qc3, and 1…Qxc4 2.Nxc4+ Kf4 3.Qxf3.  (Also, 1…Be4 2.Qxe4+, and 1…Qd3 2.Qxd3+.)
 

Intensive square strategy is found in Problem 119, particularly Black’s play that illustrates how a single move can incorporate both vacating and obstructing effects.  In this example of the logical style of more-movers, White has a course of action, called the mainplan, that fails to a certain black defence.
 

Here the plan is 1.Kg7 and 2.Nh6 mate, and if played immediately it is refuted by a discovered check, 1…Nxc4+.

White accordingly begins with a preparatory manoeuvre designed to neutralise that defence, before proceeding with the mainplan.

1.Bb7! threatens 2.Bxe4 and compels 1…Rxc4 (1…Bf3? 2.h3 leads to a quicker mate), which blocks the square needed by the knight.  However, 2.Kg7? is premature because Black’s rook move has also vacated a square for the knight – 2…Na4+! (3.Kf7 Bg7 4.Kxg7 a1(Q)+!).

Instead White continues with 2.Bc8 to threaten 3.Bxd7, inducing 2…Ba4, which obstructs the a4-square.  Now 3.Kg7? is still too early because of 3…Nd1+!, using the square vacated by the bishop.

119. Nikolai Dimitrov
Europa-Rochade 1988-89
2nd Prize

Mate in 5

Problem 120, an entertaining three-mover with many thematic variations, is for you to solve.  The solution will appear next month.

120. Christer Jonsson
Springaren 1991

Mate in 3

114. Srinivas Mantha
The Problemist 1992

Mate in 2

Black has only two legal moves in the diagram, both captures of a knight, and set mates are provided for them: 1…fxg2 2.Qh6, and 1…Kxg2 2.Qf1.

White cannot maintain this block position with a simple waiting move (in particular, any queen move will lose the focus on f1 and h6).

The key 1.Nh4! (waiting) changes Black’s play to another pair of captures, and the mating responses to these new defences are transferred from those in the set play: 1…gxh4 2.Qf1, and 1…Kxh4 2.Qh6.