The Rukhlis theme

The Rukhlis theme is one of my all time favorites. It is named after the outstanding Israeli composer Efim Rukhlis who supposedly composed over 300 examples of the theme. The Rukhlis theme incorporates changed mates and transferred mates between at least two phases. Recall that a changed mate is a different mate after the same defense. Whereas a transferred mate is the same mate after a different defense. Algebraically the Rukhlis theme has the pattern:

1st phase:
1...a 2.A
1...b 2.B

2nd phase:
1...a 2.C
1...b 2.D
1...c 2.A
1...d 2.B

The theme is known as an ideal Rukhlis if there are mates set for the transferred defenses in the first phase.  

Rukhlis, Elim
Turnier 1946

#2

9 + 9

Here is one of the most famous problems of all time maybe one of the first Rukhlis themes. The beautiful problem also shows two Grimshaws.  There is a set Grimshaw:

1...Rc4 2.Sc3
1...Bc4 2.Qe4

Notice that these mates depend on the mutual interference of the bB and bR but also on wPd3 which is blocking the lines of the bBb1 and bRh3. The key is obvious to me - anytime I see this wR and wP combination the pawn push is always the first thing I try, especially considering the potential pins on d4. However, the key has two interesting effects that usher the changes and transferences: it opens the lines of bBc1 and bRh3 but closes the lines of bRa4 and bBh8, sort of an anti-Novotny and Novotny combination.  Now the captures on c4 are self-pins and the original Grimshaw mates from d4 are transferred to a new Grimshaw on d3. Beautiful.

1.d4! (>2.Sb6)
1...Rxd4 2.Sb4
1...Bxd4 2.Sf6
1...Bd3 2.Sc3
1...Rd3 2.Qe4

Kovachevic, Marjan
Wola Gulowska 2014

#2

7 + 9

Here is one of my favorite Rukhlis problems of all time complete with cross checks, battery play, and a wR cross. The problem is an ideal Rukhlis in the sense that there are mates set for all of the thematic defenses.  There are four prominent set mates that are all changed post key

1...Rxe2 2.Re5
1...Se5 2.Rf6
1...Qa3+ 2.Re7
1...Sf6 2.Sd6

1.Sf2! (>2.Qg4)
1...Rxe2 2.Rf6
1...Se5 2.Qxe5
1...Qa3+ 2.Rd6
1...Sf6 2.Re5

Stocchi, Ottavio
Sah 1950

#2

12 + 10

Here is a famous ideal Rukhlis by one of the greatest two-move composers of all time. The set mates all display dual avoidance, particularly 1...c3 and 1...e2 which display a special kind known as Mari dual avoidance. 

1...c3 2.Sxe3
1...e2 2.Sb4
1...Sc6 2.Rd6
1...Sf5 2.Rf5

The excellent flight giving key now changes all four of these mates:

1.Se6! (>2.Qd1)
   1...c3 2.Rd4
   1...e2 2.Qd4
   1...Sc6 2.Sxe3
   1...Sf5 2.Sb4
   1...Kd6 2.Sc7

​And Sc7 is icing on the cake. 

Mari, Alberto
Alain White MT
problem (Zagreb), 1954

#2

7 + 9

Speaking of Mari, here is a gorgeous example of the theme with a royal battery and additional changes.  

1...Be4 2.Ke2
1...Bxd3 2.Kf3
1...Sc3 2.Qa7
1...d5 2.Qc5
1...Sb7 2.Qc4

1.Sc5! (>2.Qxd5)
   1...Be4 2.Rxe4
   1...Bxd3 2.Rxd3
   1...Be4 2.Ke2
   1...Sc3 2.Kf3
   1...Sb7 2.Sb3
   1...d5 2.Se6
 

Boyer, J-P. and Michel, F.
Probleme TT 1967

#2

9 + 10

In this excellent problem we have a Rukhlis with beautiful cross-checks and black correction.  

1...Bd~+ 2.Se6
1...Sc~+ 2.Se2

1.Sxe5! (>2.Sc6)
   1...Bd~+ 2.Sg6
   1...Sc~+ 2.Sd3
   1...Bxe5+ 2.Se6
   1...Sxe5+ 2.Se2
   1...Kxe5 2.Qc3

Bogdanov, Evgenij
Ryazansky Komsomolets 1982

#2

9 + 11

This problem shows the record setting Rukhlis with four transferred and changed mates. Perfunctory key is justified by the fact that it grants two checks on the wK.

1...fxe6 2.Sd7
1...Se5 2.Be7
1...Rg5 2.Rxf7
1...Rf3 2.Sxd5

1.Qxd5! (>2.Qf5)
   1...fxe6 2.Qxe6
   1...Se5 2.Qxe5
   1...Rg5 2.Qxg5
   1...Rf3 2.Se4
   1...Qd7+ 2.Sxd7
   1...Qe7+ 2.Bxe7
   1...Qxc5 2.Rxf7
​   1...Bxd5 2.Sxd5

Jönsson, Gustov
Die Schwalbe 1954

#2

10 + 9

Another wonderful ideal Rukhlis with white interference mates, white correction, and try play.

1...exf6 2.Sc2
1...f3 2.Sb3
1...Sc4 2.Rxc4
1...Sd3 2.Rxd4

1.Se~? (>2.Qe5)
    1...Qh5 2.Qg1
    1...Sd3!

1.Sg4? (>2.Qe5)
   1...Qh5!

1.Sc4! (>2.Qe5)
   1...exf6 2.Qxf6
   1...f3 2.Qe3
   1...Sc4 2.Sc2
   1...Sd3 2.Sb3
   1...Qh5 2.Qg1
   1...Sd5 2.Qxg5

At first glance it seems like the wBf8 is not used post key, however, this is not true it guards c5 after exf6.

Moen, Kabe
The Problemist 2020

#2

12 + 10

Here is one of my own with a half-battery + additional battery formation idea.  Interestingly, my problem does not fit the usual mold for a Rukhlis, because the mates after the two thematic defenses are changed but not transferred. However, my problem does have two changed mates and two transferred mates:

1.Sxe5? (>2.Sxg6)
   1...Rxd7 a 2.Sa2 A
   1...Rxh1 b 2.Sa6 B
   1...Sxe5 c 2.Bxe5 C
   1...Sg2 d 2.Qxd5 D
   1...e2!

1.Sxd5! (>2.Sf4)
    1...Rxd7 a 2.Sa3 X
    1...Rxh1 b 2.Sa5 Y
    1...Se7 x 2.Bxe5 C
    1...Sxd5 y 2.Qxd5 D
    1...Sg2 d 2.Sf6

Notice that the mates A and B are not transferred, because of this it is what might be called an extended Rukhlis.

Stojnic, Mihailo
1st Pr 8th FIDE World Cup 2020

#2

12 + 9

A fresh prize winner from the most recent World Cup for composing.  

1..Q~/.Qxg4 2.Sf6
1...dxe5 2.Sc3
1...Qf4+ 2.exf4
1...f2 2.Qh1
1...Qxe3 2.Qxe3

1.Qg3! (-)
   1...Q~ 2.Qf4
   1...Qxg4 2.Qg4
   1...dxe5 2.Qxe5
   1...Qxe3 2.Sf6
   1...f2 2.Sc3
   1...Qx53 2.Bxf5
   1...c4/cxb4 2.Rd4

It's a very nice problem but I do have some criticism.  My main complaint is the wSb4 which really has no post key function other than holding up the bPb5.  It does offer a try 1.Sc6? which contains a Dombrowski paradox, but it has an obvious refutation: 1...b4! I personally would remove -wSb4,bPb5 and shift wBd7>d8 (otherwise the matrix would be cooked by 1.Ba4).  Now-a-days it seems that problemists try to pack as much as possible into their matrices. I'm all for this, but I have strict belief of not adding material that will be useless just to create tries.  

Parthasarathy, M.
British Chess Magazine 1969

#2

9 + 11

Finally we end with a masterpiece that not only shows an ideal Rukhlis, but also the task of four changed self-blocks.  

1...Rxe6 2.Rxd4
1...Sxe6 2.c4
1...Qxe5 2.Qb3 
1...Sxe5 2.Sf4

1.Qg4! (>2.Rc5)
   1...Rxe6 2.Qxd4
   1...Sxe6 2.Qe4
   1...Sxe5 2.Rxd4 
   1...Qxe5 2.c4