05 October 2012

A few helpmates

Every now and then, I pick up some helpmates which I think are interesting. Especially when I am not in the mood for writing they are quite useful. ;-)

  1Manfred Ernst  
Problemkiste 06/2011
  2Christer Jonsson  
Vratnica-64 01-06/2008

  3Vilimantas Satkus  
The Problemist 05/2007
  4Rolf Kohring  
Mat Plus 07-12/2010

Oh yes, the solutions ...
11) 1. Nd4 Bb7 2. Nc6 Rf6+ 3. Kd5 Bxc6#
2) 1. Ng5 Rf8 2. Nf7 Bd5+ 3. Kf6 Rxf7#
21) 1. Nd5 Ba3 2. Re4 Nb4 3. Kc5 Nd3+ 4. Kd4 Bc5#
2) 1. Re6 Bg1 2. Nd5 Nf2 3. Kc5 Nd3+ 4. Kd6 Bc5#
31) 1. Kh5 Rc1 2. h1=N Rxc6 3. Nf2 Rf6 4. Ng4 Rf3 5. Rg6 Rh3#
2) 1. c5 Rb1 2. Rg6 Rxb7 3. h1=Q+ Rb1 4. Qb7 d4 5. Qg7 Rh1#
41. - f4 2. h1=B f5 3. Bd5 f6 4. Bg8 f7 5. Kb2 fxg8=Q 6. Ka3 Qb3#
1. - c4 2. Kc2 c5 3. Kd3 c6 4. Ke3 c7 5. Kf4 c8=Q 6. Kg3 Qg4#

28 September 2012

Mathematical stuff

Let's start with a construction task: create a twomover that shows the return of the piece that makes the key move as often as possible. Provided, no promoted pieces are used and no duals are allowed, the maximum seems to be 29. In 1980, Bernd Schwarzkopf had published a position with mate duals. Without knowing that, I made my own attempts (there was a little contest) about ten years laster and published a correct twomover. You'll surely find all the solutions, right?

Gerson Berlinger
32er Nr. 1-2, 1990
  29 solutions

The next diagram is a 16-in-1 problem. Have fun figuring out the solutions.

George Burt Spencer
St. Paul Dispatch, 1906
  on each file and rank

Finally, a little retro puzzle.

Nikolai Beluchow
Die Schwalbe 12/2011
By mistake, two chess positions were rotated at a random angle each and then printed onto the same chess diagram. No two pieces were printed one over the other. Separate the two positions and orientate each one correctly! (11+7)

The solution is this:
last move: f5xg6 e.p.+
last move: g7xh8=Q+

21 September 2012

The Imitator

Already a long time ago I had made plans to write about this special fairy piece. Finally, I am ready to do so.

The imitator can be compared to a shadow. It can't capture nor can it be captured nor give check. Whenever a pieces moves, the imitator moves exactly in the same way. Of course, there are some restrictions.

An imitator can't cross an occupied square except when it imitates a hopper and also has to have a hurdle. A move is illegal if it can't be accompanied by a legal move of an imitator, i.e. putting it on an occupied square (after the piece has moved) or off the board.

Normally, an imitator imitates moves of both sides, but you can also declare it to do so only when either White or Black moves. In general, the symbol is a black circle.

With more than one imitator on the board, a move is only legal, if all of them can imitate it. The promotion to an imitator is legal, but can be excluded.

The following quite simple diagram demonstrates the effect an imitator has.
Legal moves?

a) Black to move:
Rd8 (Id6)
Rc8 (Ic6)
Rb8 (Ib6)
0-0 (Ia6)
Kf8 (Ib6)+
Kf7 (Ib5)+
You can see that the imitator move is written in (round) brackets.
The imitator shields the white king from checks. Therefore, a king move puts White in check.
Moves like Ra7 or Rh5 or Ke7 are not allowed as the white king blocks the imitator.
Castling long is not possible, because the first part is the king move which is not allowed due to the position of the imitator. On the other hand, castling short works, as the imitator goes to c6 after the king move and returns to a6 after the rook move.

b) White to move:
Kb5 (Ib6)
Ka6 (Ia7)
Ka4 (Ia5)
Kb6 (Ib7)
Kb4 (Ib5)
Observe that the white knight can't move at all. It's pinned, for any move would put the white king in check which is not allowed.

Here's a composition which is easy to understand:
Rene-Jean Millour
Europe Echecs 1966
Special Prize

1. Kh2 (Ic5)! puts Black in Zugzwang:
1. - Na3 (Ia4)+ 2. Nh7 (Ic5)#
1. - Nb2 (Ib3)+ 2. Ng8 (Ic5)#
1. - Nd2 (Id3)+ 2. Ne8 (Ic5)#
1. - Ne3 (Ie4)+ 2. Nd7 (Ic5)#
1. - Ne5 (Ie6)+ 2. Nd5 (Ic5)#
1. - Nd6 (Id7)+ 2. Ne4 (Ic5)#
1. - Nb6 (Ib7)+ 2. Ng4 (Ic5)#
1. - Na5 (Ia6)+ 2. Nh5 (Ic5)#
The black pawn is blocked and any bishop move would put the black king in check, so only the black knight can move. We see a black knight wheel answered with a corresponding white knight wheel to put the imitator back to c5, so that the white king is not in check whereas its black adversary is and can't escape.