## Wednesday, April 09, 2008

### Organ Pipes

 Theme Organ Pipes: In the problem there is an arrangement of pieces (Bishop – Rook – Rook – Bishop), which is known as Organ Pipes. This arrangement forms four intersections and, theoretically, can have eight discrete thematic variations (with Grimshaw intersections).

 (Problem 34) Taverner T., First Prize, ”L’ arti”, 1881 White plays and mate in 2 moves #2 (10+7) [3brrb1/2S4B/8/2p4Q/2p2k2/5P2/4P1KR/2S2RB1]

In Taverner’s orthodox two-mover we see the arrangement B-R-R-B. We present with a condensed notation the various tries we make to solve this problem in two moves:
Tries: {1.Sd5+? Bxd5!}, {1.Se6+? Rxe6!}, {1.Sxe8? Bg5!}, {1.Qg4+? Ke5!}, {1.Qf5+? Rxf5!}, {1.e4? Bg5!}, {1.e3+? Rxe3!}, {1.Bd4? cxd4!}, {1.Sd3+? cxd3!}, {1.Rh4+? Bxh4!}, {1.Rh3? Bg5!}.

Key: 1.Rh1!
This move is not easy to find because it is not a threat, but brings black in a zugzwang situation, a situation where whatever black plays is bad for him, nevertheless black must play something.
For example, if black defend with 1...Bxh7, the square d5 stays unguarded, and white mates with 2 Sd5#. Or, if black plays 1...Re5, blocks this flight of the king allowing 2 Qg4#. If black could forfeit moving, white would not have a mating move.
Everyone of the nineteen legal answers of the black if followed instantly with mate.
The variations are : 1...c3 2.Sd3#, 1...Bxc7 2.Rh4#, 1...Bh4 2.Rxh4#, 1...Bg5 2.Qh2#, 1...Bf6 2.Qf5#, 1...Be7 2.e3#, 1...Rxe2+ 2.Sxe2#, 1...Re3 2.Bh2#, 1...Re4 2.fxe4#, 1...Re5 2.Qg4#, 1...Re6 2.Sd5#, 1...Re7 2.Rh4#, 1...Rf5 2.Qxf5#, 1...Rf6 2.Rh4#, 1...Rf7 2.Sd5#, 1...Bd5 2.Sxd5#, 1...Be6 2.e3#, 1...Bf7 2.Qf5#, 1...Bxh7 2.Sd5# .

The thematic approach in finding the solution is to observe that in the initial position black is almost in zugzwang.
If black is forced to play first, only two moves exist (Re3 and Bg5) without a mate. But, each of these moves blocks a critical flight of the black king. The move Re3 blocks the square e3 that is guarded by Bg1, and the move Bg5 blocks the square g5 that is guarded by Qh5.
After removing properly the rook from h2, white will be able to bring Bg1 or Qh5 on this square to give mate: 1...Re3 2.Bh2# and 1...Bg5 2.Qh2# .

The arrangement Organ Pipes (B-R-R-B) is well known to problemists, who understand that the black pieces will have mutual interferences during the solution. For example, see what happens when black play 1...Bf7. White now mates with 2.Qf5#, a move made possible only because the black bishop cut the action of black Rf8, which were guarding f5. We call self-interference what black B makes to black R.
Similarly, if black answers 1...Rf7, this creates interference on the guarding of d5 by Bg8. The result is that white gives mate with 2.Sd5#. Mutual interferences like this, between two black pieces (of dissimilar linear movement) on an empty square, characterize the Grimshaw intersections.
There are four Grimshaw intersections in this problem, (but the solution does not achieve the task of eight different mate pictures, it shows only four: Qf5#, Sd5#, e3#, Rh4#).

Grimshaw intersection on f7 : 1...Bf7 / Rf7 2.Qf5# / Sd5#
Grimshaw intersection on e6 : 1...Be6 / Re6 2.e3# / Sd5#
Grimshaw intersection on e7 : 1...Be7 / Re7 2.e3# / Rh4#
Grimshaw intersection on f6 : 1...Bf6 / Rf6 2.Qf5# / Rh4#

[This post in Greek language].