I always enjoy David Shire's problems and this one is no different. In this problem the innocuous twinning changes the strategy from a threat to a waiting problem.  Both solutions are very satisfying with a flight giving key and gate openings.  The problem also has a nice bit of detective work that must be done to figure out why one solutions hold in each part 

(a) 1.Sc3 (>2.Qc8)
     1...Kxc3 2.Qd3
     1...Rd5 2.Qxd5
     1...Rd6 2.Qb5

(b)  1.Ka4! (-)
      1...a5 2.Qb5
      1...Rd5 2.Qc2
      1...Rd3 2.exd3
      1...R~ 2.Sa3

Here is one of my earlier compositions and a nice little block problem at that.  The twinning is slightly unusual in that you have to solve part (a) before proceeding to (b).  (a) has a flight giving key while (b) is a complete block with with several obstruction tries and an added mate.

(a) 1.Bg4! (-)
         1...Ke4 2.Qxc4
         1...Sg~ 2.Sf5
         1...Bg2 2.Qxg2
         1...Bf3 2.Bxf3
         1...Be4 2.Be6

For part (b) the problem is a complete block so all White has to do is find a waiting move to hold the fort.

(b) 1.Ba8? c5!  1.Be3? Ke4! 1.Bf2? Bg2!
     1.Bg2! (-)
         1...c5 2.Qa8

Part (b) has a neat little key in which the wB is shuttled to the edge of the board without much effort.  Solvers commented that it could stand alone!

Here is another curiosity: the two kings are swapped.  It is interesting because the wK plays such a prominent role in the first part.

1.Rxc2! (-)
   1...Bd2 2.Kxd2
   1...bxc2 2.Kxc2
   1...Bxe3 2.Kxe3
   1...S~ 2.Ke4

1.Qc6! (-)
   1...Bd2 2.Re1
   1...Bxe3 2.Rxf2
   1...Bxb2 2.Sxb2
   1...S~ 2.Qg6
   1...Se4 2.Qc4

​Neat total change and battery play.

Something brilliant from the great composer.  A random move of the wK will threaten Rf8. Surely the type of piece on a3 can't determine the key move?!  Notice the set mate after castling          1...0-0-0 2.Qxc7, which uses the wBg2's guard on c7.

(a) 1.Kg1! (>2.Rf8)
(b) 1.Ke1! (>2.Rf8)
(c) 1.Ke3! (>2.Rf8) (Kg1 is a nice try here)

Now we come to the interesting part.  The only reasonable square for the wK to go is g3, but this destroys the set mate after 1...0-0-0.  However, castling is illegal!  Why?  Black has 7 pawns and the bBb3 is promoted.  This means that the bQ must have escaped her home square somehow and the only way is if the bK has moved.  Castling is illegal!

(d) 1.Kg3!

Not a lot of play but a beautiful and rich idea with a wK star.  The twinning mechanism is the so called Forsberg twinning in which a piece of different type is substituted.

This is a continual form of twinning in which the alterations are made to the new diagram.  In this particular case the procedure continuously removes pieces, giving the so-called strip-tease twinning. The problems are as follows:

(a) diagram
(b) remove a2
(c) further remove c2
(d) further remove b2
(e) further remove c3

(a) 1.Qd3!
(b) 1.Kd3!
(c) 1.Rc4!
(d) 1.Qa2!
(e) 1.Kd3!

Achieving sound problems in each part is amazing.

​

 
​This problem appeared next to one of my own (also a twin) in the British Chess Magazine.  Usually moving the bK is an unwanted form of twinning, but here we get a changed double Grimshaw.  

(a) 1.b8=S! (-)
         1...Be7 2.R6e5
         1...Re7 2.Sf6
         1...Be2 2.R3e5
         1...Re2 2.Bxf3
         1...Rxe6 2.Bxe6
         1...Rxe3 2.Sxe3
         1...c6 2.Rd6

(b) 1.Sf8! (-)
         1...Be7 2.R6e4
         1...Re7 2.Rf6
         1...Be2 2.R3e4
         1...Re2 2.Rxf3
         1...Rxe6 2.Sxe6
         1...Rxe3 2.Bxe3
         1...c6 2.Bd6

Remarkably there is a hidden task to this problem.  There seven pairs of mates on the same square.  The squares d6, e3, e4, e5, e6, f3, and f6 are all visited by two different white pieces for mate. I really like the interchange of functions between the bishops and the knights.

Another ingenious idea from the Hungarian Grandmaster.  Loyd introduced the excelsior in 1861 and this is a two move take on the idea.  One could argue to leave off (e) because of the repeated mate Qxf3, but I like the knight promotion coupled with the Q promotion in the previous part.

(a) 1.a4! Kxc6 2.Be4
(b) 1.a5! Kxc6 2.Qxf3
(c) 1.a6! Kxc6 2.Qc5
(d) 1.a7! Kxc6 2.a8=Q
(e) 1.a8=S! Kxc6 2.Qxf3

Another sparkling idea.  A bK shift leads to reciprocally changed mates between a Grimshaw with play to the same square.  The mechanism is a change between direct and indirect batteries.  Maybe the only flaw is the identical keys.

(a) 1.Ba6! (>2.Qd3,Qf4) 
   1...Bc4 2.Sc5
   1...Rc4 2.Bc5

(b) 1.Ba6! (>2.Qd3,Qe5)
   1...Bc4 2.Bc5
   1...Rc4 2.Sc5

Another classic from Mansfield that won first prize in the Problemist.  A stalemate release with lots of changes.

(b) wK>d7
(c) wK>g3
(d) wK>g5
(e) wK>f8
(f) wK>a3

​(a) 1.Bc3! Kc4 2.Ba2
(b) 1.Rf6! Ke5 2.Rf5
(c) 1.Rc2! Ke4 2.Rc5
(d) 1.Kf6! Kd4 2.Ke6
(e) 1.Bg6! Ke6 2.Be4
(f) 1.Bc2! Kc4 2.Be4

I wasn't going to include any helpmates in this post but this one is too good to pass up.  One of the most original ideas I have ever seen.  I am going to call this the time machine theme.  I have included the full algebraic notation so you can understand the idea.

(a) 1.Sd6-f5 Sd7-e5 2.Rc6-d6 Se5-f7 3.Bb5-d7 Sf7-d8
(b) 1.Bd7-b5 Sd8-f7 2.Rd6-c6 Sf7-e5 3.Sf5-d6 Se5-d7

Here is one of my original ideas that features board manipulation.  This is probably the heaviest position I have created but I think the idea is worth it.  The idea is that in the set play of (a) bPe6 controls the royal battery.  So it must be captured after the self pinning check.  After the key this square is now occupied.  When the board is inverted this strategy is reciprocally changed to the other pawn.  Between all of the variations and threats there is a wK tour.

(a)
   1...Sxf5+ 2.Kxe6
1.Bxe6! (>2.Kd7)
   1...Sxf5+ 2.Kxc6
   1...Sxe6 2.Kxe6
   1...Rxc5 2.Kxc5
   1...Sf6 2.Ke7
   1...Bxb6 2.Bxd2

(b)
   1...Sxf4+ 2.Kxc3
1.Bxc3! (>2.Kd4)
   1...Sxf4+ 2.Kxe3
   1...Sxc3 2.Kxc3
 
It's not a big deal but looking back I wish I would have rotated the board 180 degrees instead of reflecting it.  Why?  In terms of a physical chess board a rotation makes more sense.  After all, if you flip over a board then all of the pieces would fall off!

          

Another board manipulation problem.  I like the way manipulating the board affects castling.  This problem features a non-partial 4-fold Fleck in each part.  That is, each twin makes 4 threats and there are 4 unique moves that separate the threats. All other moves purposely give all 4 threats.  The only downfall is the flight taking key in (b).  Interestingly the key pieces play to the same square in each part.

(a) 1.Bg4! (>2.Kd2,Ke2,Kf2,0-0)
           1...cxd4 2.Kd2
           1...Kc1 2.Ke2
           1...c3 2.Kf2
           1...Rh8 2.0-0

(b) 1.Kg4! (>2.Bg5,Bf6,Be7,Bd8)
           1...e2 2.Bg5
           1...b5 2.Bf6
           1...Ra7 2.Be7
​           1...Ra8 2.Bd8

A nice example in miniature form.  It is clear that the wQ or wR must get to the h-file to deal with KxS...but how should they approach?

1.Rc4? (Rc2? etc) (-)
  1...Be5 (B any) 2.Qg6
  1...Kxh6 2.Rh4
  1...Bg7!

1.Qc4? (Qa4) (-)
  1...Be5 (B any) 2.Qe4
  1...Kxh6 2.Qh4
  1...Bd4!

Finally it is clear that the wQ should approach the h-file along a white square diagonal.

1.Qc8! (-)
  1...Be5 2.Qf5
  1...Kxh5 2.Qh3s

Stocchi made several Zagoruikos and can be credited with popularizing the theme.  Here the two thematic defenses are both interferences 1...g6 and 1...Bb2, both placing guard on d4 but interfering with the bRs.

1...g6 2.Se6
1...Bb2 2.Sb3

1.Sf5? (>2.Qd4)
   1...g6 2.Bd6
   1...Bb2 2.Bb6
   1...Rb4!

The refutation gives a hint to the key which places guard on b4.

1.Sc2! (>2.Qd4)
  1...g6 2.Qxc6
  1...Bb2 2.Qb4
  1...Sb4 2.Qc4
​  1...cxd5 2.Sd3

Quite possibly one of the most outstanding Zagoruikos, let alone, two-movers ever by the great Russian composer. One can criticize the unprovided flight, but it is necessary for the mechanism to work.

1...Rxd5 2.Qc2
1...Sxd5 2.Bxf5

To handle the flight KxR White must move the wS on d4.  Doing so creates a threat of Rd4.

1.Se6? (>2.Rd4)
  1...Rxd5 2.Sg5
  1...Sxd5 2.Sxc5
  1...f4!

1.Sxf5? (2.Rd4)
  1...Rxd5 2.Qxe3
  1...Sxd5 2.Sd6
  1...Sd7!

1.Sc6! (2.Rd4)
  1...Rxd5 2.Sg5
  1...Sxd5 2.Sd2
  1...Kxd5 2.Qd3
  1...Rc4 2.Re5

A 4x2 Zagoruiko!  Perfection on a chess board.

Here's one by the man himself.  A nice open near Meredith with interference changes.  Chunky pieces with no white pawns.

1...Sc2 2.Bc6
1...Sf3 2.Bf7

1.Se6? (>2.Qd4)
   1...Sc2 2.Sc7
   1...Sf3 2.Sf4
   1...Rc4!

1.Sb3? (>2.Qd4)
   1...Sc2 2.Qc5
   1...Sf3 2.Qe4 (this time the bS interferes with the bB)

1.Se2! (>2.Qd4)
   1...Sc2 2.Sc3
   1...Sf3 2.Sf4
   1...Rc4 2.Qd6

Excellent work.

An ambitious Zagoruiko in block form with flight giving try and key.  

1...e2 2.Bd4
1...b5 2.Re6
1...Sf4 2.Qg7
1...Sf6 2.Qg3

1.Rd6? (-)
  1...e2 2.Re6
  1...b5 2.Sd7
  1...Sf4 2.Qf6
  1...Sf6 2.Qg3
  1...bxc5!

1.Rd4! (-)
   1...e2 2.Sd7
   1...b5 2.Re4
   1...Sf6 2.Qf4
   1...Sf4 2.Qg7
   1...Sb~ 2.Rd5

This is what is called a reduced Zagoruiko because the mate Sd7 is transferred between different defenses, that is, a 3x2 Zagoruiko should have 6 different mates after the defenses, but this one only has 5.

  

Here is another form of reduced Zagoruiko the cyclic Zagoruiko or Rice cycle after J.M. Rice's famous problem (Problem 37th TT 1961 yacpdb.org/#371177). The pattern is the following:

1st phase
1...x 2.A
1...y 2.B

2nd phase
1...x 2.B
1...y 2.C

3rd phase
1...x 2.C
1...y 2.A

This problem also shows what is called the Ellerman-Makarov theme: there are three set mates for 1...Ke6 and the tries each separate these mates. 
​
1...Ke6 2.Qxb3/Qe3/Qf4

But there are no mates set for random moves of the bS.

1.Ra3? (-) 
   1...Ke6 2.Qf4
   1...S~ 2.Qxb3
   1...Se3!
1.Bh6? (-)
   1...Ke6 2.Qxb3
   1...S~ 2.Qe3
   1...Sf4!
1.Sf2! (-)
   1...Ke6 2.Qe3
   1...S~ 2.Qf4
   1...e5 2.Rxd5
   1...f4 2.Qe4

The idea is that to compensate for random moves of the bS White must give up guard of a square in the bK's extended field.  This will determine which mate works after 1...Ke6. If not for the unused wBh1 post-key this would be probably the best problem on this entire blog.

​

This is a Zagoruiko in three move form.  The key 1.Qxc6 threatens 2.e5+ Be4 3.Rf1.  Black can defend by moving the bRb7 to open the bQ's line, but each move will interfere with the bB or bQ in some way and the thematic defenses are 2...Qxe4 and 2...Kxe4.

1.Qxc6! (>2.e5+ Be4 3. Rf1)
  1...Rb6 2.Qc5 (>3.Qe3)
      2...Kxe4 3.Rg3
      2...Qxe4 3.Qf2
  1...Rxa7 2.Qxb5 (>3.Qe2)
​      2...Kxe4 3.Rg4
      2...Qxe4 3.Qf1
​  1...Rb8 2.Qd7 (>3.Qg4)
​      2...Kxe4 3.Re2
      2...Qxe4 3.Qh3
​  1...Rxc7 2.Qd6 (>3.Qf4)
​      2...Kxe4 3.Rf2
      2...Qxe4 3.Qg3

An amazing problem.  Interestingly, this play is shown as in multiphase form in the following two-mover by Lobusov (The Problemist 1976 yacpdb.org/#30150)

One of the greatest achievements in the Zagoruiko framework: a 3x4.  The wQ is adroitly placed for 4 set mates, these are changed in the try and then changed again after the key.

1...c5 2.Qa8
1...e5 2.Qg8
1...Rxg2 2.Qxd6
1...cxd2 2.Rc5

1.Qf6? (>2.Qd4)
   1...c5 2.Sb4
   1...e5 2.Qf7
   1...Rxg2 2.Qxf3
   1...cxd2 2.Sf4
   1...Rg4!

1.Qb6! (>2.Qd4)
   1...c5 2.Qb7
   1...e5 2.Sf4
   1...Rxg2 (Rg4) 2.Sb4
   1...cxd2 2.Qxc6
​

Finally here is my only Zagoruiko - which pales in comparison to the above problems.  The problem is a zeroposition which means the diagram is not for solving but must be altered.  The twinnings are:
 
(a) bRc1 > g3
(b) wRe1 > d1
(c) wBg7 > f8

The problem was entered in a theme tourney for Newotny (New ideas in the Novotny) in honor of John Rice, Barry Barnes, Michael Lipton, and Colin Sydenham's 80th birthdays and received a commendation. The judge Wieland Burch writes:

"The same key and the same defenses three times over – not something that’s usually desirable... But here this gives rise to three distinct types of Nowotny: first the standard form, then a paradoxical Nowotny with reciprocal change of the mates, and finally a Romanian Nowotny with the captures as total defenses  The result is a 3x2 Zagoruiko."

(a) 1.d4! (>2.Qc4,Qe5)
          1...Bxd4 2.Qc4
          1...Rxd4 2.Qe5

(b) 1.d4! (>2.Qc4,Qe5)
          1...Bxd4 2.Qe5
          1...Rxd4 2.Qc4

(b) 1.d4! (>2.Qc4,Qe5)
          1...Bxd4 2.Sb4
          1...Rxd4 2.Sf6