Series auto-stalemates with the Equistopper

(Vaclav Kotesovec, 13.6.2024)

I have always been interested in auto-stalemates, but the possibilities of such chess problems are quite limited. It is necessary that White's last move must not be able to be made the same way back. In orthodox chess (if we only have white pieces on the board) this can only be achieved when the last move is a pawn move. Without pawns and without fairy conditions this can be achieved with e.g. Mao or Moa pieces (for example P1379418), but even here the possibilities are rather limited.

In May 2024, Sébastien Luce inspired me when in an e-mail he brought to my attention the Equistopper piece, which also has this property. I extended his original idea of using multiple of these same pieces to different combinations of material and discovered a lot of length records. In particular, when combined it with the ABC condition (Alphabétiques), the possibilities of such problems are associated with a number of different specific motifs that are used to achieve dual free solutions.


Definitions:
  • Series auto-stalemate (sd-auto=n, ser-!=n in Popeye): White plays a series of n moves concluding in stalemate to White.
  • Non-stop equistopper (ES): makes moves which are halfway to any other unit (the hurdle) in any direction, irrespective of any other units between it and the hurdle.
  • For clarification, it should be noted that, throughout this article, the term "Equistopper" refers to the so-called "Non-stop equistopper", called also "French Equistopper" (in WinChloe marked as "Equistopper", in Popeye QF).
  • Wazir: [0,1]-leaper.
  • Alphabetic chess (ABC chess, Alphabétiques): Each move of either side must be by the piece occupying the first square in the order of a1, a2, a3, ... , b1, b2, b3, ..., c1, c2, c3, ... etc., which is able to make a legal move. Castling is permitted if the King has the right to make a legal alphabetical move, provided the usual other rules for that move are obeyed.


  • ES01 Vaclav Kotesovec, original
    (dedicated to Sebastien Luce)
    White QFa8f8d6a4b4a3a2a1h1
    ser-!=50
    AlphabeticChess
    9 non-stop equistoppers
    C+
    1.QFa2-a5 2.QFa1-a2 3.QFa4-a6 4.QFa2-a4 5.QFa6-a7 6.QFa4-a6 7.QFa3-a4 8.QFb4-c5 9.QFa5-b5 10.QFa4-a5 { } 11.QFa7-b6 12.QFa6-a7 13.QFa5-a6 14.QFb5-e3 15.QFb6-c6 16.QFa6-b6 17.QFa8-b7 18.QFb6-d7 19.QFa7-b6 20.QFb7-e4 { } 21.QFc5-d4 22.QFb6-c5 23.QFc6-d5 24.QFd4-e6 25.QFc5-d4 26.QFd5-f3 27.QFd4-d5 28.QFd6-e7 29.QFd5-d6 30.QFd7-f4 { } 31.QFd6-e5 32.QFf3-g2 33.QFe4-f3 34.QFe3-e4 35.QFf4-f6 36.QFe6-f4 37.QFe5-e6 38.QFe4-e5 39.QFf4-f5 40.QFe6-f4 { } 41.QFe5-e6 42.QFf5-g3 43.QFe7-f5 44.QFf6-f7 45.QFf4-f6 46.QFe6-f4 47.QFf7-g4 48.QFf6-f7 49.QFf4-f6 50.QFf3-f4 {autopat}

    This is an absolute record with 9 ES. My program VKComposer needed 317 CPU hours to explore all the possibilities!

    Testing of chess problems with ES is possible only with WinChloe or Popeye. Alybadix does not know this piece. However, due to the ABC condition, testing these problems is very fast, usually only a few seconds, a few minutes at most.


    ES01B Vaclav Kotesovec, original
    White QFa8f8d6a4b4a3a2a1
    ser-!=21
    AlphabeticChess
    9 non-stop equistoppers
    C+
    Some may now think that ESh1 is redundant in the previous position. It is not! Without ESh1, the problem has a shorter solution in 21 moves, and it is surprising that this solution is unambiguous!

    1.QFa2-a5 2.QFa1-a2 3.QFa4-a6 4.QFa2-a4 5.QFa6-a7 6.QFa4-a6 7.QFa3-a4 8.QFb4-c5 9.QFa5-b5 10.QFa4-a5 { } 11.QFa7-b6 12.QFa6-a7 13.QFa5-a6 14.QFb6-c6 15.QFa6-b6 16.QFa8-b7 17.QFb6-d7 18.QFa7-b6 19.QFb7-c7 20.QFd6-e7 21.QFc5-d6 {autopat}



    ES02 Vaclav Kotesovec, original
    White Kd1 QFa8a4h1
    ser-!=25
    AlphabeticChess
    3 non-stop equistoppers
    C+
    1.QFa4-a6 2.QFa6-a7 3.Kd1-d2 4.Kd2-d3 5.Kd3-d4 6.Kd4-d5 7.Kd5-d6 8.Kd6-d7 9.Kd7-e8 10.QFa8-c8 { } 11.QFc8-d8 12.Ke8-f7 13.Kf7-g8 14.Kg8-h8 15.QFd8-f8 16.QFf8-g8 17.Kh8-h7 18.QFh1-h4 19.Kh7-g7 20.QFa7-d7 { } 21.Kg7-h8 22.QFh4-h6 23.QFh6-h7 24.QFd7-f7 25.QFf7-g7 {autopat}

    A simple problem (Wenigsteiner), in which White's king has a clear path through the centre of the open chessboard, suprisingly unambigous. For example, if White were to move 4.Kc3, he would no longer be able to move the king, because (given the ABC condition) the move 5.ESa7-b5 would have to follow, etc.


    ES03 Vaclav Kotesovec, original
    White Kd1 QFa8a4h2b1
    ser-!=43
    AlphabeticChess
    4 non-stop equistoppers
    C+
    1.QFa4-a6 2.QFa6-a7 3.QFb1-c1 4.QFa7-b4 5.QFb4-e3 6.QFc1-d2 7.Kd1-c1 8.Kc1-b2 9.Kb2-c3 10.Kc3-d4 { } 11.QFd2-d3 12.Kd4-c3 13.Kc3-d2 14.Kd2-e1 15.Ke1-f2 16.Kf2-g3 17.QFe3-f3 18.QFd3-e3 19.Kg3-f4 20.Kf4-f5 { } 21.QFf3-f4 22.QFf4-g3 23.QFe3-f3 24.QFf3-f4 25.Kf5-f6 26.QFf4-f5 27.Kf6-e7 28.Ke7-f8 29.Kf8-g8 30.QFa8-d8 { } 31.Kg8-h8 32.QFd8-f8 33.QFf8-g8 34.QFh2-h5 35.QFf5-g5 36.QFg3-g4 37.QFg4-g6 38.QFg6-g7 39.QFg5-g6 40.Kh8-h7 { } 41.QFh5-h6 42.Kh7-h8 43.QFh6-h7 {autopat}



    ES04 Vaclav Kotesovec, original
    White Ka4 QFa8b3b2a1h1
    ser-!=63
    AlphabeticChess
    5 non-stop equistoppers
    C+
    1.Ka4-a5 2.QFa1-a3 3.QFa3-a4 4.QFa4-a6 5.Ka5-a4 6.Ka4-a3 7.Ka3-a2 8.Ka2-b1 9.QFa6-a7 10.Kb1-a2 { } 11.Ka2-a3 12.Ka3-a4 13.Ka4-a5 14.Ka5-a6 15.Ka6-b7 16.QFb3-b5 17.QFb5-e3 18.QFa7-c5 19.Kb7-c7 20.QFc5-d4 { } 21.QFb2-c3 22.QFc3-d3 23.Kc7-d7 24.QFd3-d5 25.QFd5-f3 26.Kd7-e8 27.QFa8-c8 28.QFc8-d8 29.QFd4-d6 30.QFd6-d7 { } 31.QFd7-e5 32.QFe3-e4 33.QFe4-e6 34.QFe6-e7 35.QFe5-e6 36.Ke8-d7 37.Kd7-d6 38.Kd6-e5 39.Ke5-f4 40.QFf3-g2 { } 41.Kf4-g4 42.QFe6-f5 43.QFf5-g3 44.QFe7-f5 45.Kg4-g5 46.QFg3-g4 47.QFf5-g3 48.Kg5-g6 49.QFg4-g5 50.QFg2-g4 { } 51.Kg6-g7 52.QFg5-g6 53.QFg3-g5 54.Kg7-h8 55.QFd8-f8 56.QFf8-g8 57.QFg6-g7 58.QFg4-g6 59.Kh8-h7 60.QFh1-h4 { } 61.Kh7-h8 62.QFh4-h6 63.QFh6-h7 {autopat}



    ES05 Vaclav Kotesovec, original
    White Ka4 QFb8d3a2b2a1h1
    ser-!=67
    AlphabeticChess
    6 non-stop equistoppers
    C+
    1.QFa2-a3 2.QFa1-a2 3.Ka4-b5 4.Kb5-a6 5.QFa2-a4 6.QFa4-a5 7.QFa3-a4 8.Ka6-b5 9.Kb5-b4 10.QFb2-b3 { } 11.QFb3-c3 12.Kb4-b5 13.QFa5-b4 14.QFb4-b6 15.Kb5-c6 16.QFa4-b5 17.QFb5-c4 18.QFb6-b7 19.QFb7-c5 20.Kc6-c7 { } 21.QFc5-c6 22.QFc3-c5 23.Kc7-d8 24.QFb8-c8 25.QFc6-c7 26.QFc4-c6 27.QFd3-f2 28.Kd8-d7 29.Kd7-d6 30.Kd6-e5 { } 31.QFc5-d5 32.QFc7-d6 33.QFc6-c7 34.QFd5-f3 35.QFd6-e4 36.QFc7-d6 37.Ke5-d5 38.Kd5-c6 39.Kc6-d7 40.Kd7-e7 { } 41.Ke7-f7 42.QFf3-f5 43.QFf5-g3 44.Kf7-g8 45.QFc8-e8 46.QFe4-f6 47.QFd6-e6 48.QFe6-f7 49.QFe8-f8 50.QFf2-f5 { } 51.QFf7-g4 52.QFf6-f7 53.QFf5-f6 54.QFg4-g6 55.QFf7-g4 56.QFf6-f7 57.QFg4-g5 58.QFf7-g4 59.QFg6-g7 60.QFg4-g6 { } 61.QFg3-g4 62.Kg8-h7 63.QFh1-h4 64.Kh7-h8 65.QFf8-g8 66.QFh4-h6 67.QFh6-h7 {autopat}



    ES06 Vaclav Kotesovec, original
    White Ka6 QFc8b7f5c4a2b2h1
    ser-!=78
    AlphabeticChess
    7 non-stop equistoppers
    C+
    1.QFa2-a4 2.QFa4-a5 3.Ka6-b5 4.Kb5-a4 5.Ka4-b3 6.Kb3-c2 7.QFb7-e4 8.Kc2-b3 9.Kb3-a4 10.Ka4-b5 { } 11.Kb5-a6 12.Ka6-a7 13.QFa5-a6 14.QFa6-b7 15.Ka7-b8 16.QFb2-b5 17.QFb5-b6 18.QFb7-d6 19.QFb6-b7 20.Kb8-a7 { } 21.Ka7-b6 22.Kb6-c5 23.QFc4-c6 24.Kc5-d4 25.QFc6-c7 26.Kd4-e5 27.Ke5-f4 28.QFd6-e5 29.QFb7-d6 30.Kf4-f3 { } 31.Kf3-g2 32.QFe4-f3 33.QFf3-f4 34.QFf5-g3 35.Kg2-h3 36.QFh1-h2 37.Kh3-g2 38.Kg2-f3 39.Kf3-e4 40.Ke4-d5 { } 41.Kd5-c6 42.Kc6-d7 43.Kd7-e7 44.QFc7-d7 45.QFe5-e6 46.QFd6-e5 47.Ke7-f6 48.QFf4-f5 49.QFe5-f4 50.Kf6-g5 { } 51.QFg3-g4 52.QFf4-g3 53.Kg5-h4 54.QFh2-h3 55.Kh4-g5 56.Kg5-f6 57.Kf6-e7 58.Ke7-f8 59.Kf8-g8 60.QFc8-e8 { } 61.QFe6-f7 62.QFd7-e7 63.QFe8-f8 64.QFf5-f6 65.QFe7-f5 66.QFf7-g5 67.QFf6-f7 68.QFf5-f6 69.QFg4-g6 70.QFg3-g4 { } 71.QFg6-g7 72.QFg4-g6 73.Kg8-h7 74.QFh3-h5 75.QFh5-h6 76.Kh7-h8 77.QFf8-g8 78.QFh6-h7 {autopat}

    Positions after 36. and 54. move create a chameleon echo.


    ES07 Vaclav Kotesovec, original
    White Se1 QFe6a5a2c2h1
    ser-!=51
    AlphabeticChess
    5 non-stop equistoppers
    C+
    1.QFa2-b2 2.QFa5-c3 3.QFc2-d4 4.QFc3-d2 5.QFb2-c3 6.QFd2-d3 7.QFc3-d2 8.QFd3-f2 9.QFd2-d3 10.QFd4-e3 { } 11.Se1-f3 12.Sf3-e5 13.QFe3-e4 14.Se5-c4 15.Sc4-e3 16.Se3-g2 17.QFe4-e5 18.QFe6-f4 19.QFf2-f3 20.QFd3-e3 { } 21.QFe3-e4 22.Sg2-e3 23.Se3-c4 24.Sc4-d6 25.Sd6-f7 26.QFf3-f5 27.QFf5-g3 28.Sf7-h6 29.QFf4-g5 30.QFe5-f4 { } 31.QFg3-g4 32.Sh6-f5 33.Sf5-g3 34.Sg3-h5 35.QFh1-h3 36.QFh3-h4 37.Sh5-f6 38.QFf4-f5 39.QFe4-f4 40.Sf6-d7 { } 41.Sd7-f8 42.QFf4-f6 43.QFf6-f7 44.QFf5-f6 45.Sf8-g6 46.Sg6-h8 47.QFf6-g7 48.QFg5-g6 49.QFg4-g5 50.QFh4-h6 51.QFh6-h7 {autopat}



    ES08 Vaclav Kotesovec, original
    White Sd1 QFd3a2d2h2a1h1
    ser-!=61
    AlphabeticChess
    6 non-stop equistoppers
    C+
    1.Sd1-b2 2.Sb2-a4 3.QFa2-a3 4.QFa1-a2 5.Sa4-b6 6.Sb6-a8 7.QFa2-a5 8.QFa3-a4 9.QFa4-a6 10.QFa6-a7 { } 11.QFa5-a6 12.Sa8-b6 13.Sb6-a4 14.Sa4-b2 15.Sb2-d1 16.Sd1-f2 17.QFd2-e2 18.QFa6-c4 19.Sf2-d1 20.Sd1-b2 { } 21.Sb2-a4 22.Sa4-b6 23.Sb6-c8 24.QFc4-c6 25.QFc6-c7 26.QFa7-b7 27.QFb7-e4 28.Sc8-b6 29.Sb6-c4 30.Sc4-d2 { } 31.Sd2-f3 32.QFd3-e3 33.QFc7-d5 34.Sf3-d4 35.Sd4-f5 36.QFd5-e5 37.Sf5-d6 38.Sd6-e8 39.QFe4-e6 40.QFe2-e4 { } 41.QFe6-e7 42.QFe4-e6 43.QFe3-e4 44.Se8-d6 45.Sd6-f7 46.Sf7-h8 47.QFh2-h5 48.QFh1-h3 49.QFh3-h4 50.QFh4-h6 { } 51.QFh6-h7 52.QFh5-h6 53.Sh8-g6 54.QFe4-f5 55.QFe6-f6 56.QFe5-e6 57.Sg6-h8 58.QFf5-g6 59.QFf6-g7 60.QFe6-f6 61.QFe7-f7 {autopat}

    The white knight's long path across the board.


    ES09 Vaclav Kotesovec, original
    White Sf2 QFa6h5a4a2b2a1h1
    ser-!=63
    AlphabeticChess
    7 non-stop equistoppers
    C+
    1.QFa2-a3 2.QFa1-a2 3.QFa4-a5 4.QFa2-a4 5.QFb2-d2 6.QFd2-e2 7.QFa4-c3 8.QFa3-a4 9.QFa5-b4 10.QFa4-a5 { } 11.QFa6-c4 12.QFb4-d3 13.QFa5-b4 14.QFd3-f4 15.QFb4-d3 16.Sf2-d1 17.Sd1-b2 18.Sb2-a4 19.Sa4-b6 20.Sb6-c8 { } 21.QFc4-c6 22.QFc6-c7 23.QFc3-c5 24.QFc5-c6 25.QFc6-d4 26.Sc8-d6 27.QFd3-f2 28.QFd4-d5 29.QFd5-f3 30.Sd6-f5 { } 31.QFf3-g4 32.QFe2-f3 33.QFf3-g2 34.QFf2-f3 35.Sf5-d4 36.Sd4-e6 37.Se6-f8 38.QFf4-f6 39.QFf6-f7 40.QFf3-f5 { } 41.QFf5-f6 42.QFf7-g6 43.QFf6-f7 44.Sf8-d7 45.Sd7-e5 46.QFc7-d6 47.Se5-c6 48.Sc6-e7 49.Se7-g8 50.QFg2-g5 { } 51.QFg6-g7 52.QFf7-g6 53.Sg8-e7 54.Se7-c6 55.Sc6-e5 56.Se5-f7 57.Sf7-h8 58.QFd6-f7 59.QFh1-h3 60.QFh3-h4 { } 61.QFh4-h6 62.QFh6-h7 63.QFh5-h6 {autopat}



    ES10 Vaclav Kotesovec, original
    White Rc2 QFb8f8b5c4a3g2
    ser-!=59
    AlphabeticChess
    6 non-stop equistoppers
    C+
    1.QFb8-d8 2.Rc2-b2 3.Rb2-b4 4.Rb4-a4 5.Ra4-a8 6.Ra8-c8 7.QFc4-c6 8.QFc6-e4 9.Rc8-c2 10.Rc2-e2 { } 11.QFd8-e8 12.Re2-d2 13.Rd2-d3 14.QFb5-c4 15.QFc4-d4 16.Rd3-b3 17.Rb3-b6 18.Rb6-d6 19.QFd4-d5 20.Rd6-c6 { } 21.Rc6-c1 22.QFa3-b2 23.Rc1-c6 24.Rc6-e6 25.QFe4-e5 26.Re6-g6 27.QFe8-f5 28.QFg2-g4 29.QFg4-g5 30.Rg6-c6 { } 31.Rc6-c2 32.Rc2-d2 33.QFb2-c2 34.Rd2-e2 35.QFc2-d2 36.Re2-e3 37.Re3-f3 38.QFd5-e4 39.Rf3-d3 40.Rd3-d4 { } 41.QFd2-d3 42.Rd4-d6 43.Rd6-h6 44.QFf8-g7 45.QFe5-f6 46.QFf6-g6 47.Rh6-h8 48.Rh8-d8 49.Rd8-d7 50.QFd3-d5 { } 51.QFd5-d6 52.Rd7-e7 53.Re7-e8 54.QFe4-e6 55.QFe6-e7 56.QFe7-f7 57.Re8-e6 58.Re6-f6 59.QFd6-e6 {autopat}

    One would expect the white rook to be blocked in a corner of the board, but instead it ends up in the middle of the board.


    ES11 Vaclav Kotesovec, original
    White Rb7 QFc8a6c2a1b1d1f1
    ser-!=65
    AlphabeticChess
    7 non-stop equistoppers
    C+
    1.QFa6-b4 2.QFb1-c1 3.QFa1-b1 4.Rb7-a7 5.Ra7-a3 6.Ra3-b3 7.QFb1-b2 8.Rb3-a3 9.Ra3-a7 10.Ra7-b7 { } 11.QFb2-b3 12.QFb3-b5 13.QFb5-b6 14.QFb4-b5 15.QFb5-d3 16.Rb7-a7 17.Ra7-a3 18.Ra3-c3 19.QFc2-c5 20.QFc1-c2 { } 21.Rc3-a3 22.Ra3-a7 23.Ra7-d7 24.QFd1-d4 25.QFd3-d5 26.QFd5-e3 27.Rd7-a7 28.Ra7-a4 29.Ra4-c4 30.QFc2-c3 { } 31.QFc3-d3 32.Rc4-c2 33.Rc2-f2 34.QFd3-e2 35.QFc8-d5 36.Rf2-f3 37.QFd5-e4 38.QFf1-f2 39.Rf3-h3 40.Rh3-h1 { } 41.Rh1-g1 42.Rg1-g2 43.QFe4-f3 44.Rg2-g1 45.Rg1-a1 46.Ra1-a7 47.Ra7-d7 48.Rd7-d5 49.Rd5-h5 50.QFf3-g4 { } 51.QFe2-f3 52.Rh5-d5 53.Rd5-d7 54.Rd7-b7 55.Rb7-b8 56.QFb6-b7 57.QFb7-d5 58.Rb8-e8 59.QFd5-e4 60.QFe4-e6 { } 61.QFe6-f5 62.Re8-e4 63.Re4-f4 64.QFd4-e4 65.QFc5-d4 {autopat}

    As in the previous problem, there is a final stalemate position in the middle of the board.


    Of course, if we use other fairy pieces, even longer lengths can be achieved. However, that would be beyond the scope of this article. For the sake of illustration, I will give just one such position.

    ES12 Vaclav Kotesovec, original
    White QFh8a6b3g2a1b1c1 WEa4
    ser-!=113
    AlphabeticChess
    7 non-stop equistoppers
    1 wazir
    C+
    1.WEa4-a3 2.QFa1-a2 3.QFa2-a4 4.WEa3-a2 5.WEa2-b2 6.QFa4-a5 7.QFa6-d4 8.WEb2-a2 9.WEa2-a3 10.WEa3-a4 { } 11.WEa4-b4 12.QFb1-b2 13.QFb2-c3 14.WEb4-a4 15.WEa4-a3 16.WEa3-a2 17.WEa2-b2 18.QFa5-b4 19.WEb2-a2 20.WEa2-a3 { } 21.WEa3-a4 22.WEa4-a5 23.WEa5-a6 24.WEa6-b6 25.QFb4-b5 26.QFb3-b4 27.QFb4-e6 28.WEb6-a6 29.WEa6-a7 30.WEa7-a8 { } 31.WEa8-b8 32.WEb8-c8 33.QFc1-c2 34.QFc2-c5 35.QFc3-c4 36.QFc4-c6 37.QFc6-e4 38.WEc8-b8 39.WEb8-a8 40.WEa8-a7 { } 41.WEa7-a6 42.WEa6-b6 43.WEb6-c6 44.WEc6-d6 45.QFd4-d5 46.WEd6-c6 47.WEc6-b6 48.WEb6-a6 49.WEa6-a7 50.WEa7-a8 { } 51.WEa8-b8 52.WEb8-c8 53.WEc8-d8 54.WEd8-e8 55.QFe4-e5 56.QFe6-f4 57.WEe8-d8 58.WEd8-c8 59.WEc8-b8 60.WEb8-a8 { } 61.WEa8-a7 62.WEa7-a6 63.WEa6-b6 64.WEb6-c6 65.WEc6-d6 66.WEd6-e6 67.WEe6-f6 68.QFf4-f5 69.WEf6-g6 70.QFg2-g4 { } 71.QFg4-g5 72.WEg6-h6 73.WEh6-h5 74.WEh5-h4 75.WEh4-g4 76.WEg4-f4 77.WEf4-e4 78.WEe4-d4 79.WEd4-d3 80.QFb5-c4 { } 81.WEd3-d2 82.WEd2-e2 83.QFc4-d3 84.QFd3-e4 85.WEe2-f2 86.WEf2-f3 87.WEf3-f4 88.WEf4-g4 89.QFe4-f4 90.QFf4-g6 { } 91.WEg4-f4 92.WEf4-e4 93.WEe4-d4 94.WEd4-c4 95.WEc4-b4 96.WEb4-b5 97.WEb5-b6 98.WEb6-c6 99.WEc6-d6 100.WEd6-d7 { }101.QFd5-d6 102.QFc5-d5 103.QFd6-f7 104.QFd5-d6 105.WEd7-d8 106.QFd6-d7 107.QFd7-e7 108.WEd8-d7 109.WEd7-d6 110.WEd6-e6 { }111.WEe6-f6 112.QFe5-e6 113.QFh8-g7 {autopat}



    ES13 Vaclav Kotesovec, original
    White Rd8 Sb1 QFf7a5a1d1
    ser-!=60
    AlphabeticChess
    4 non-stop equistoppers
    C+
    1.QFa1-a3 2.QFa3-a4 3.Sb1-a3 4.Sa3-b5 5.Sb5-c7 6.QFa5-b6 7.Sc7-a6 8.QFa4-a5 9.Sa6-b8 10.QFb6-b7 { } 11.QFb7-c4 12.Sb8-a6 13.Sa6-b4 14.Sb4-d3 15.QFd1-d2 16.QFd2-d5 17.Sd3-b4 18.Sb4-c2 19.Sc2-d4 20.Sd4-e6 { } 21.Rd8-b8 22.Rb8-b3 23.Rb3-c3 24.QFa5-b4 25.Rc3-a3 26.Ra3-a6 27.Ra6-c6 28.QFc4-c5 29.Rc6-d6 30.Rd6-d7 { } 31.QFd5-d6 32.Rd7-b7 33.Rb7-b6 34.QFb4-b5 35.Rb6-b8 36.Rb8-g8 37.Se6-d4 38.Sd4-c6 39.Sc6-e7 40.Se7-g6 { } 41.Sg6-h8 42.Rg8-a8 43.Ra8-a1 44.Ra1-f1 45.QFb5-d3 46.QFd3-e2 47.Rf1-f5 48.Rf5-h5 49.QFf7-g6 50.QFd6-f7 { } 51.QFe2-f4 52.Rh5-f5 53.Rf5-f6 54.QFf4-f5 55.Rf6-e6 56.Re6-e7 57.QFc5-d6 58.Re7-e6 59.Re6-f6 60.QFd6-e6 {autopat}

    See ES19 for a similar problem with two solutions.


    ES14 Vaclav Kotesovec, original
    White Sh8b6 QFa8a4f4a2a1c1
    ser-!=40
    AlphabeticChess
    6 non-stop equistoppers
    C+
    1.QFa1-b1 2.QFa2-a3 3.QFa3-b2 4.QFa4-a6 5.QFa6-a7 6.QFa7-b4 7.QFb2-e5 8.QFb4-d4 9.Sb6-a4 10.Sa4-b2 { } 11.Sb2-d1 12.QFc1-d3 13.QFb1-c1 14.Sd1-b2 15.Sb2-a4 16.Sa4-b6 17.Sb6-c8 18.QFa8-b8 19.QFb8-e8 20.Sc8-a7 { } 21.Sa7-c6 22.Sc6-d8 23.QFd4-d6 24.QFd6-f7 25.Sd8-b7 26.Sb7-d6 27.Sd6-e4 28.Se4-f6 29.QFf4-g6 30.Sf6-e4 { } 31.Se4-f2 32.Sf2-h1 33.QFd3-f2 34.QFc1-d3 35.QFf2-g5 36.QFd3-f2 37.QFe5-f5 38.QFf5-g3 39.QFf7-g4 40.QFe8-f7 {autopat}

    Interestingly, there does not exist a stalemate position with 4 ES + 2 knights and even with 5 ES + 2 knights, 6 ES is necessary!


    ES15 Vaclav Kotesovec, original
    White Ka2 Rg7e3 QFc8d1h1
    ser-!=46
    AlphabeticChess
    3 non-stop equistoppers
    C+
    1.Ka2-b3 2.Kb3-c4 3.Kc4-d5 4.QFd1-d3 5.QFd3-d4 6.Kd5-e5 7.Re3-f3 8.Ke5-f5 9.Rf3-f2 10.QFd4-e3 { } 11.Rf2-d2 12.Rd2-d8 13.Rd8-e8 14.QFc8-d8 15.Re8-e7 16.QFe3-e5 17.QFe5-e6 18.Re7-f7 19.Kf5-f4 20.Kf4-g3 { } 21.Rf7-f5 22.Rf5-h5 23.Kg3-h3 24.Rg7-f7 25.Rf7-f8 26.QFd8-e8 27.QFe6-e7 28.Rf8-f7 29.Rf7-h7 30.QFh1-h2 { } 31.Kh3-h4 32.QFh2-h3 33.Kh4-g5 34.QFe7-f6 35.Kg5-f5 36.Kf5-e6 37.Ke6-f7 38.Kf7-g7 39.Kg7-h8 40.QFf6-g7 { } 41.QFh3-h4 42.QFh4-h6 43.Rh5-f5 44.Rf5-f8 45.Rf8-g8 46.QFe8-f8 {autopat}



    ES16 Vaclav Kotesovec, original
    White Rg6a3a2 QFa8b2h2
    ser-!=34
    AlphabeticChess
    3 non-stop equistoppers
    C+
    1.Ra2-a1 2.Ra1-b1 3.Ra3-a7 4.Ra7-d7 5.Rb1-a1 6.Ra1-a6 7.Ra6-b6 8.QFb2-b4 9.QFb4-e3 10.Rb6-b8 { } 11.Rb8-e8 12.QFa8-c8 13.QFc8-d8 14.Rd7-d5 15.Rd5-f5 16.Re8-e5 17.QFe3-e4 18.Re5-e7 19.Re7-g7 20.Rf5-f8 { } 21.QFd8-e8 22.QFe4-e6 23.QFe6-e7 24.QFe7-f7 25.Rf8-h8 26.Rg6-h6 27.Rg7-h7 28.QFf7-g7 29.QFh2-h5 30.Rh6-f6 { } 31.Rf6-f8 32.Rf8-g8 33.QFe8-f8 34.QFh5-h6 {autopat}



    ES17 Vaclav Kotesovec, original
    White Kf1 Sb1 QFd8a4a2h2a1
    ser-!=74
    AlphabeticChess
    5 non-stop equistoppers
    C+
    1.QFa2-a3 2.QFa1-a2 3.Sb1-d2 4.Sd2-b3 5.Sb3-d4 6.Sd4-b5 7.Sb5-a7 8.QFa3-a5 9.QFa2-a3 10.QFa5-a6 { } 11.QFa3-a5 12.Sa7-b5 13.Sb5-d4 14.Sd4-b3 15.Sb3-c1 16.QFa5-b3 17.QFa4-a5 18.QFb3-d2 19.QFa5-b3 20.Sc1-a2 { } 21.Sa2-c3 22.Sc3-a4 23.Sa4-c5 24.Sc5-b7 25.QFb3-b5 26.QFb5-b6 27.QFb6-c7 28.Sb7-c5 29.Sc5-d7 30.QFd2-f2 { } 31.Sd7-f8 32.QFd8-e8 33.Kf1-e2 34.QFa6-c4 35.QFc4-d6 36.QFd6-e4 37.Ke2-e3 38.QFc7-d5 39.Ke3-d4 40.Kd4-c5 { } 41.Kc5-d6 42.Kd6-e6 43.QFe4-e5 44.Ke6-f6 45.QFf2-f5 46.Kf6-g5 47.Sf8-e6 48.Se6-c5 49.Sc5-e4 50.Se4-f6 { } 51.Sf6-g8 52.QFe8-f8 53.Kg5-h5 54.QFf5-g5 55.QFd5-f5 56.Sg8-f6 57.Sf6-d5 58.Sd5-f4 59.Sf4-g6 60.Sg6-h8 { } 61.QFf8-g8 62.Kh5-g6 63.Kg6-f6 64.Kf6-e7 65.QFe5-e6 66.QFe6-f7 67.Ke7-f6 68.Kf6-g6 69.QFf5-f6 70.QFf6-g7 { } 71.Kg6-h7 72.QFg5-g6 73.QFh2-h5 74.QFh5-h6 {autopat}



    ES18 Vaclav Kotesovec, original
    White Ka2 Rb1 Sc6 QFd8a6h5a1
    ser-!=67
    AlphabeticChess
    4 non-stop equistoppers
    C+
    1.Ka2-b3 2.QFa6-b6 3.Rb1-b2 4.Rb2-a2 5.Ra2-a4 6.Ra4-b4 7.Kb3-a4 8.Ka4-b5 9.Rb4-a4 10.Ra4-a7 { } 11.QFa1-a4 12.Ra7-c7 13.Kb5-a6 14.QFa4-a5 15.Ka6-b5 16.Kb5-c4 17.Kc4-d3 18.Sc6-b4 19.Sb4-d5 20.Rc7-a7 { } 21.QFa5-a6 22.Ra7-a8 23.QFa6-a7 24.Ra8-b8 25.QFb6-b7 26.QFb7-c6 27.Rb8-b1 28.Rb1-c1 29.QFa7-b4 30.Rc1-f1 { } 31.Kd3-c4 32.Kc4-b5 33.Kb5-a6 34.Ka6-b7 35.Kb7-c7 36.Kc7-d7 37.Sd5-e3 38.Kd7-e7 39.Se3-f5 40.Ke7-f7 { } 41.Rf1-f3 42.Rf3-h3 43.Sf5-g3 44.Kf7-g7 45.Sg3-h1 46.Kg7-h7 47.Sh1-g3 48.Sg3-f5 49.Sf5-e7 50.Se7-g8 { } 51.QFc6-e7 52.QFb4-c6 53.Sg8-f6 54.Sf6-d7 55.Sd7-e5 56.Se5-f7 57.Sf7-h8 58.QFd8-f8 59.QFf8-g8 60.Rh3-f3 { } 61.Rf3-f7 62.Rf7-g7 63.QFe7-f7 64.QFc6-e7 65.QFf7-g6 66.QFe7-f7 67.QFh5-h6 {autopat}

    This problem was the only one that was a bit more challenging to test. WinChloe took 4 hours 34 minutes and Popeye took 1 hour 41 minutes.


    ES19 Vaclav Kotesovec, original
    White Rf8 Sb1 QFd7e6f5a1
    ser-!=12
    4 non-stop equistoppers
    2 solutions
    C+
    1.Rf8-e8 2.QFe6-e7 3.QFe7-c4 4.Re8-e3 5.QFa1-c2 6.Re3-c3 7.QFf5-d3 8.Sb1-d2 9.Sd2-b3 10.QFd7-c5 11.Sb3-a1 12.QFc5-b3 {autopat} 1.Sb1-c3 2.QFa1-b2 3.Sc3-e2 4.QFe6-e4 5.QFe4-e3 6.Se2-g3 7.Sg3-h1 8.QFf5-g3 9.Rf8-f3 10.QFd7-f4 11.QFb2-d3 12.QFd3-f2 {autopat}

    A chameleon echo in two corners of the chessboard.

    The attentive reader will not have missed the fact that this problem is without the ABC condition. Unfortunately, the possibilities of such positions are rather limited and the length records much shorter than with the ABC condition (compare with ES13). Moreover, for problems with one solution, the play is usually less interesting.


    ES20 Vaclav Kotesovec, original
    White Ra1 QFb6b4a3c2
    ser-!=21
    AlphabeticChess
    4 non-stop equistoppers
    4 solutions
    C+
    1.Ra1-d1 2.QFb4-b5 3.QFb5-c3 4.QFa3-b3 5.Rd1-e1 6.QFc3-d2 7.QFb6-c4 8.QFc2-c3 9.Re1-e7 10.QFc3-d5 { } 11.Re7-e1 12.Re1-f1 13.QFd5-e3 14.Rf1-a1 15.Ra1-a6 16.Ra6-c6 17.QFc4-c5 18.QFc5-d4 19.Rc6-c3 20.Rc3-d3 21.QFb3-c3 {autopat} 1.Ra1-e1 2.QFb4-b5 3.Re1-b1 4.Rb1-b4 5.Rb4-a4 6.Ra4-a8 7.Ra8-d8 8.QFb6-c7 9.Rd8-f8 10.Rf8-f7 { } 11.QFb5-d6 12.QFa3-b5 13.Rf7-f4 14.QFd6-e5 15.QFc7-d6 16.Rf4-c4 17.QFc2-c3 18.QFc3-d4 19.Rc4-c5 20.Rc5-d5 21.QFb5-c5 {autopat} 1.Ra1-g1 2.QFa3-d2 3.QFb4-c3 4.QFb6-c4 5.QFc3-e2 6.QFc2-c3 7.QFc4-d3 8.Rg1-g6 9.QFe2-f4 10.QFd2-e3 { } 11.Rg6-c6 12.Rc6-c5 13.QFc3-c4 14.Rc5-c7 15.Rc7-d7 16.QFd3-d5 17.QFd5-d6 18.QFd6-e5 19.Rd7-d4 20.Rd4-e4 21.QFc4-d4 {autopat} 1.Ra1-h1 2.QFb4-b5 3.QFb5-e3 4.QFa3-c3 5.QFc3-d3 6.QFd3-f2 7.QFb6-d4 8.Rh1-h4 9.QFd4-f4 10.QFf2-f3 { } 11.QFf4-g4 12.Rh4-h6 13.Rh6-e6 14.QFc2-d4 15.Re6-e7 16.QFe3-e5 17.QFe5-e6 18.QFe6-f5 19.Re7-e4 20.Re4-f4 21.QFd4-e4 {autopat}

    Quadruple echo with final stalemate positions in the middle of the chessboard.

    But I regret the repetitive second move of White, so I am publishing the problem only in the article and not sending it to a competition.




    Diagrams created with Py2Web