Reciprocal Change

Reciprocal change is a difficult and paradoxical idea in chess composition.  It happens when two mates are interchanged between the same two defenses between two phases.  In algebraic terms: In one phase mate A follows defense X while mate B follows defense Y.   In another phase mate B follows X and mate A is switched to defense Y.  Even though I have not had much success at it, reciprocal change is one of my favorite themes.  We begin with a crystal clear example by Barry Barnes. 

Barnes, Barry
Sunday Times 1964

#2

5 + 7

Here reciprocal change is effortlessly executed in Meredith. Using bK flight squares is a common, but striking way to pull of reciprocal change.  We have relevant set play:

   1...Kxf5 2.Rxe3
   1...Ke4 2.Rxd5

The pendulum type key threatens mate on e6 and now the mates are swapped after the bK moves:

1.Qb6! (>2.Qe6)
   1...Kxf5 2.Rxd5
   1...Ke4 2.Rxe3

In order to pull off reciprocal change one needs two effects after the key: the new mates must work and the old mates must fail.  In this case obviously the wQ plays a crucial role.  Before the key she guards the squares d5 and g5 and she gives these up for guard on e3 and e6.  

Sydenham, Colin
Mat Plus 1995

#2

8 + 10

In this problem we have a similar set up with an indirect battery aimed at the bK flights.  Moreover, each of these flights is set with a dual:

   1...Kd4 2.Rd3/Rc5
   1...Ke5 2.Rd3/Rc5

The try and key separate the duals and reciprocally change them.  Here the mechanism is uses the guard on the squares f5 and c4 and the opening of black lines to swap the mates.

1.Sge4? (>2.Qd6)
   1...Kd4 2.Rd3
   1...Ke5 2.Rc5
1.Sde4! (>2.Qd6)
   1...Kd4 2.Rc5
   1...Ke5+ 2.Rd3

Einat, Paz
Isreal Ring Tourney 1975

#2

10 + 6

Here we have a doubling of the theme.  A common mechanism for reciprocal effects is the forming of batteries: should the rear piece play first forming the battery or should the front piece play and clear the way for the rear piece.  In this amazing problem we see this strategy to perfect.  We see two possible Q+R batteries to be formed one with the wQ to f1 and another with wR capturing e6.  However, we can move the front piece for two nice tries.  

1.Re3 X? (>2.Rc3)
   1...Sxa4 2.Qf1 A
   1...Sd7 2.Qxe6 B
   1...Qh8!
1.Re5 Y? (>2.Rxc5)
   1...Sxa4 2.Qxe6 B
   1...Sd7 2.Qf1 A
   1...Qf2!
1.Qf1 A? (>2.Re4)
   1...Sxa4 2.Re3 X
   1...Sd7 2.Re5 Y
   1...Sd3!
1.Rxe6! (>2.Re4)
   1...Sxa4 2.Re5 Y
   1...Sd7 2.Re3 X
   1...Sxe6 2.Qxe6
   1...Qd4 2.Rxd4

Bwee, Touw Hian
Die Schwalbe 1982

#2

b) Bh1 to h5

8 + 8

Here we have a twinning mechanism to achieve reciprocal change.  The reciprocally changed mates come from two different knights playing to the same square.  

a) 1.Qb5 (>2.Qb3)
   1...Se2 2.Sfe5
   1...Se4 2.Sce5

b) 1.Qa4 (>2.Qb3)
   1...Se2 2.Sce5
   1...Se4 2.Sfe5

Bwee, Touw Hian
Probleemblad 1983

#2

7 + 9

Another great but simple reciprocal change by Indonesian composer.  Here the change is based on the focal control of the bQ on the long diagonal.  

1.d7? (>2.d8=Q)
   1...Qf6 2.Qxh1
   1...Qg7 2.Qxb7
   1...c3!

1.Bg6! (>2.Bf7)
   1...Qf6 2.Qxb7
​   1...Qg7 2.Qxh1

Bruch, Wieland
Schach-Report 1992

#2

b) f5=bR

7 + 7

This is probably one of the most original mechanisms for reciprocal change that I have ever seen.  The problem uses a so called Forsberg twinning to replace a piece by different piece of the same color.  The goal in each part is to guard c2 so that the wBg8 can mate on c4 by closing the wR's line.  

(a)
1.Sa1! (>2.Bc4)
   1...e6 2.Qd7
   1...e5 2.Rd6
   1...Sf7 2.Qxf5
   1...Be4+ 2.Qxe4

(b)
1.Sa3 (>2.Bc4)
   1...e6 2.Rd6
   1...e5 2.Qd7
   1...Sf7 2.Qxf5

In addition to reciprocal change we have two Gamage unpins.  It's amazing how the whole problem works and why the guards on c3 and d4 dictate the defenses and keys in each part.  

Einat, Paz
StrateGems 2016

#2

13 + 9

We have a wonderful prize winning problem.  Notice the wR,wS, and wB on the e-file.  This is what is known as a half-battery.  Guarding e6 (in particular if any move of wSe7 or wBe6) will threaten 2.Sf7.  However, something must be done about the defense 1...Sg5.  Let's try moving the wQ first.

1.Qa2? (>2.Sf7)
   1...Qxe7 2.Qd5
   1...Qxe6 2.Qxe6
   1...Sg5 2.Qh2
   but 1...Bxe3

This almost works but the wQ abandoned her access to e3.  Now it is obvious that we should move the wBe6 or wSe7. Let's try the wB which should go to f5 (why?)

1.Bf5? (>2.Sf7)
   1...Qxe7 2.Qc5 (2.Qd4?)
   1...Qe6 2.Qd4 
   1...Sg5 2.f4 (notice the wB now guards e4)
   1...Bxe3 2.Qxe3
   but 1...Qd5!

1.Sg8!
   1...Qe7 2.Qd4
   1...Qxe6 2.Qc5 (2.Qd4?)
   1...Sg5 2.Bxf6
   1...Bxe3 2.Qxe3
   1...Qxd7 2.Bxd7

Thus we see the half-battery theme, reciprocal change, and a 3x3 Zagoruiko (3 different mates after the defenses 1...Qe7,Qe6,Sg5).  Wow!

Moen, Kabe
SuperProblem 2017

#2

b) bQd2 to g3

10 + 6

We end with my reciprocal change problem which is obtained by means of twinning.  The twins have the same key, which can be considered a flaw, but here it might be a feature.  Part a) is a usual Novotny whereas part b) is what I call a reversed Novotny.  The reciprocal change happens by pinning and line opening, i.e., if the bQ is removed from the board then after the captures of the key pawn on d4 both mates Bb3 and Qxe5  would work.  However, in part a) she blocks the wRd1's line so only the standard Novotny mates work, where as in part b) the moves of the bBc3 and bRf4 open the bQ's lines so the other mates are the ones that work.  One thing that was really important to me was working in the defense 1...Qe3 2.Sxf4 in part a) so that the wRd1 was utilized.

a)
1.d4! (>2.Bb3 A/Qxe5 B)
   1...Bxd4 2.Bb3 A
   1...Rxd4 2.Qxe5 B
   1...Qe3 2.Sxf4
   1...Kxe6 2.Qf7

b) 
1.d4! (>2.Bb3 A/Qxe5 B)
   1...Bxd4 2.Qxe5 B
   1...Rxd4 2.Bb3 A