[Retros] Last move Type D

[Mario Richter]

Dear Retrofans,

on January 20, among other news Otto announced:

> - Last move Records: ... type D has been deleted.


That's rather a pity, because I was just working on
on a contribution on exactly that topic.

Without owning a big library of old problem magazins, it was
a little bit difficult to get the necessary information, but
finally I got the data, which I now want to present to you,
combined with some questions/challenges, where I invite you
to contribute.


1. History
==========

The idea of Lastmovers Type D was introduced by Bernd Schwarzkopf
during the Andernach meeting 1981.
During that meeting and shortly afterwards some problem friends
dealt with that idea and provided some record constructions,
which were collected by B.Schwarzkopf and finally published in
an article in 'feenschach' Nr.64 (1983).


2. Definition
=============

Last move records refer to positions, in which the last move
is uniquely determined.
They are classified according to the following additonal
constraint:

Type A: it is not given, which side has the move
Type B: it is given,which side has the move, but the king
        of the side to move is not allowed to be in check.
Type C: check is allowed.

B.Schwarzkopf's idea now was to add some kind of 'duplex'
stipulation to Type B - that is, a Last move problem of Type D
is defined as following:

A Lastmover Type D is a position, in which both
- under the assumption, that White has the move, Black's last
  move is uniquely determined
as well as
- under the assumption, that Black has the move, White's last
  move is uniquely determined

Like Type A-C, the records are classified according to the
nature of the uniquely determined last move, e.g. BxR, PxQ=R, K-
and so on. But because two last moves play a role, the number
of potential Last move records Type D is approx. 1770.
(59x58/2 + 59).


3. Prior art
============

B.Schwarzkopf found two older problems with different stipulations,
which also have the Type D property, and which therefore can be
considered as the earliest examples of Last move type D problems:

U. Grinblat, problem November 1957
RNk5/Kppp4/p7/8/8/8/8/8

Original stipulation: White moved last. How?

Considered as a Type D problem, it is of type NxR/KxN/8 (the last
number being the total count of pieces on the board).

The other prior art problem is:

Luis Alberto Garaza, Probleemblad 1956
1BRb4/b1R1p3/N7/KpPP4/pPkrP3/r1NpRP2/P1p1Pp2/1B1b4

Original stipulation: #2, Duplex

Considered as a Type D problem, it is of type P--/P--/27.


4. The list of records
======================

The following list contains all the 'feenschach' problems with the
exception of those which turned out to be incorrect:

P-/P-/ 8    8/8/8/8/8/4P1P1/3Prp1P/5K1k
Wolfgang Dittmann

KxN/KxN/10    8/8/8/8/8/4P3/2PPRPPP/3BK2k
Bernd Schwarzkopf

N-/P-=B/15    8/8/8/8/8/1PP1P3/PP1BRPP1/NkbRKB2
Hemmo Axt

B--/B--/22    n7/p1pp1p2/1p5P/bP4pK/kP4pB/p5P1/2P1PP1P/7N
Bernd Schwarzkopf  (an improvement with respect to Garaza's position)

K-/K-/17    5knn/4ppb1/5pRb/6p1/8/8/PPPP1PP1/K7
Wolfgang Dittmann

K-/B-/17    6nn/4ppbk/5pRb/6p1/8/8/PPPP1PP1/K7
Wolfgang Dittmann

K-/Q-/19    6nn/4ppqk/5prb/6p1/8/8/PPPPPPPP/7K
Bernd Schwarzkopf

K-/R-/19    5bnn/4ppr1/5pRb/6p1/8/5P2/PPPPP1P1/k1K5
Wolfgang Dittmann

QxN/QxN/12    8/8/8/8/8/6P1/PPPP1PRP/q1QK1k2
Bernd Schwarzkopf

QxN/RxN/12    8/8/8/8/8/6P1/PPPP1PRP/r1QK1k2
Bernd Schwarzkopf

R-/N-/13    8/8/8/8/7P/4PPkr/3PP1bR/4bRKn
Bernd Schwarzkopf

RxN/B-/10    8/8/8/8/1P6/kPP5/bRrP4/K1B5
Günter Eder, Günter Büsing, Hans Peter Rehm, Hemmo Axt

RxN/RxN/ 9    8/8/8/8/8/P7/KPkPP3/R1rb4
Bernd Schwarzkopf

B-/B-/17    8/8/8/8/8/3PPPPP/1PPrR1RB/2brBkbK
Bernd Schwarzkopf
(remark: Here both with White to move and Black to move
         the last 3 single moves are uniquely determined)

B-/BxN/14    3BbKBk/2ppr1rb/4pppp/8/8/8/8/8
Wolfgang Dittmann, Hans Gruber, Günter Büsing, Bernd Schwarzkopf

BxN/BxN/13    3BBKbk/2ppr1rb/4ppp1/8/8/8/8/8
Wolfgang Dittmann, Hans Gruber, Günter Büsing, Bernd Schwarzkopf

B-/N-/ 9    3Bb1kN/2ppK1pp/3p2p1/8/8/8/8/8
Bernd Schwarzkopf

N-/N-/12    8/8/8/8/8/3PP3/kPPRrP2/NbnK4
Bernd Schwarzkopf

K-/N-/18    5bkn/4pprn/5pp1/8/8/8/PPPPPPPP/7K
Bernd Schwarzkopf

K-/P-/13    K4nkn/pp1p1prp/2p1p1p1/8/8/8/8/8
Günter Büsing, Günter Lauinger, Wolfgang Dittmann, Bernd Schwarzkopf

K-/P--/21    6nk/1P2p2p/BRPPPP1P/1ppppppK/8/8/1P1P4/8
Bernd Schwarzkopf

KxN/NxQ/17    8/8/8/8/7P/5PPR/PPPPPrkb/3KnrNR
Bernd Schwarzkopf

Q-/R-/15    3BQ1rk/2pRPbrB/3ppKpp/8/8/8/8/8
Bernd Schwarzkopf

Q-/Q-/15    3BQ1qk/2pRPbrB/3ppKpp/8/8/8/8/8
Bernd Schwarzkopf

R-/R-/15    3BR1rk/2pRPbrB/3ppKpp/8/8/8/8/8
Bernd Schwarzkopf

N-/P--/22    6bN/1P3p1k/BrPPPP2/1ppppppK/7p/8/1PP4P/8
Bernd Schwarzkopf

N-/PxN/13    8/8/8/8/8/P2PP3/pPPrRP2/KBNk4
Bernd Schwarzkopf

KxN/P-=B/ 9    8/8/8/8/8/8/kPPP1P2/bRK1b3
Hans Gruber, Bernd Schwarzkopf

NxR/PxN=R/13    8/8/8/8/8/2PPP3/P1PKRPP1/rk1NB3
Wolfgang Dittmann, Hans Gruber, Günter Büsing, Bernd Schwarzkopf

P-/P-=B/ 9    8/8/8/8/8/6P1/2P1PP1P/3bRK1k
Bernd Schwarzkopf

P-/P-=N/11    8/8/8/8/8/5P1P/1PP1PRP1/nRK1k3
Bernd Schwarzkopf

P-=B/P-=B/28    nrbqkb1B/1Pppppp1/1p6/8/8/6P1/1PPPPPp1/b1BQKBRN
Bernd Schwarzkopf
(remark: Here both with White to move and Black to move
         the last 8 single moves are uniquely determined)

So far the list of problems published in the above mentioned
'feenschach' article.


Here's one, published more than 20 years later:

KxN/KxB/12    8/8/8/8/8/3P1P2/1PPRPrPP/2B1k2K
Bernd Schwarzkopf (S2 Problemkiste 153 (June 2004), p. 532


and here two contructed by me:

N-/K-/ 9    5K1N/3prppk/4p2p/8/8/8/8/8
Mario Richter
(an improvement of the above N-/K- position from feenschach)

K-/PxN/11    8/8/8/8/8/1PPP4/KpPRP3/Bnk5
Mario Richter


5. Open questions / challenges
==============================

- Are there other 'prior art' examples?

- Are there other Type D problems published after
  the introductery article in 'feenschach'?

- Are there Type D positions with less than 8 pieces?
  (8 pieces is the current record, see above W.Dittmann's
   P-/P- record)

- Can at least all Type D records be found, where Black's
  and White's last move is of the same nature?

- Are there combinations of White's/Black's last move,
  which are definitively not possible (e.g. 0-0/* - but
  others too might be impossible)?

- Are there Type D positions, where the sequence of
  uniquely defined last moves is longer than Schwarzkopf's
  record of length 8?

- Can you find other Type D positions with 12 or less pieces?


6. Acknowledgements
===================

I'd like to thank Bernd Schwarzkopf and Wolfgang Dittmann.
Without their help the above article would not have been
possible.


Regards,

   mario