Stalemate problems of record length with Locust and PlatzWechselCirce

(Vaclav Kotesovec, 15.6.2023)

The face to face white Locust versus a group of black Grasshoppers in PWC offers a lot of possibilities:
  • trying to find length records in sd=n or h=n or looking for interesting patterns during the solution(s).
  • To reach the stalemate, each time, white by successive captures has to scatter black Grasshoppers all over the board, to deprive them of any hurdle.
  • The most interesting stipulation for it h=n as both kinds of fairy pieces are playing together.

  • What is the longest series direct stalemate and helpstalemate with material Locust against several Grasshoppers (without kings) ?
    The following computer-generated table gives a complete answer to this question.

    SDP1 Vaclav Kotesovec, original
    (dedicated to Sebastien Luce)
    white Lc2 black Gc6d6e6c5d5c4d4d3
    Locust - 8 Grasshoppers

    1.Lc2*d3-e4[+bGc2] 2.Le4*c2-b1[+bGe4] 3.Lb1*e4-f5[+bGb1] 4.Lf5*e6-d7[+bGf5]{ } 5.Ld7*c6-b5[+bGd7] 6.Lb5*c4-d3[+bGb5] 7.Ld3*f5-g6[+bGd3] 8.Lg6*d6-c6[+bGg6]{ } 9.Lc6*c5-c4[+bGc6] 10.Lc4*d4-e4[+bGc4] 11.Le4*d3-c2[+bGe4] 12.Lc2*c4-c5[+bGc2]{ } 13.Lc5*d5-e5[+bGc5] 14.Le5*e4-e3[+bGe5] 15.Le3*e5-e6[+bGe3] 16.Le6*e3-e2[+bGe6]{ } 17.Le2*c2-b2[+bGe2] 18.Lb2*b5-b6[+bGb2] 19.Lb6*c6-d6[+bGb6] 20.Ld6*e6-f6[+bGd6]{ } 21.Lf6*d6-c6[+bGf6] 22.Lc6*c5-c4[+bGc6] 23.Lc4*c6-c7[+bGc4] 24.Lc7*d7-e7[+bGc7]{ } 25.Le7*c7-b7[+bGe7] 26.Lb7*e7-f7[+bGb7] 27.Lf7*b7-a7[+bGf7] 28.La7*b6-c5[+bGa7]{ } 29.Lc5*c4-c3[+bGc5] 30.Lc3*f6-g7[+bGc3] 31.Lg7*f7-e7[+bGg7] 32.Le7*c5-b4[+bGe7]{ } 33.Lb4*c3-d2[+bGb4] 34.Ld2*e2-f2[+bGd2] 35.Lf2*d2-c2[+bGf2] 36.Lc2*b2-a2[+bGc2]{ } 37.La2*a7-a8[+bGa2] 38.La8*a2-a1[+bGa8] 39.La1*b1-c1[+bGa1] 40.Lc1*c2-c3[+bGc1]{ } 41.Lc3*g7-h8[+bGc3] 42.Lh8*c3-b2[+bGh8] 43.Lb2*b4-b5[+bGb2] 44.Lb5*b2-b1[+bGb5] {=}

    Absolute length record with this material.

    SDP2 Vaclav Kotesovec, original
    white Lc1 black Gd6c5c4d4d3e3c2f2
    Locust - 8 Grasshoppers

    1.Lc1*c2-c3[+bGc1] 2.Lc3*d4-e5[+bGc3] 3.Le5*e3-e2[+bGe5] 4.Le2*f2-g2[+bGe2]{ } 5.Lg2*e2-d2[+bGg2] 6.Ld2*d3-d4[+bGd2] 7.Ld4*d6-d7[+bGd4] 8.Ld7*d4-d3[+bGd7]{ } 9.Ld3*c3-b3[+bGd3] 10.Lb3*c4-d5[+bGb3] 11.Ld5*c5-b5[+bGd5] 12.Lb5*b3-b2[+bGb5]{ } 13.Lb2*d2-e2[+bGb2] 14.Le2*d3-c4[+bGe2] 15.Lc4*d5-e6[+bGc4] 16.Le6*e5-e4[+bGe6]{ } 17.Le4*e6-e7[+bGe4] 18.Le7*d7-c7[+bGe7] 19.Lc7*e7-f7[+bGc7] 20.Lf7*c7-b7[+bGf7]{ } 21.Lb7*b5-b4[+bGb7] 22.Lb4*c4-d4[+bGb4] 23.Ld4*e4-f4[+bGd4] 24.Lf4*d4-c4[+bGf4]{ } 25.Lc4*f4-g4[+bGc4] 26.Lg4*e2-d1[+bGg4] 27.Ld1*c1-b1[+bGd1] 28.Lb1*b2-b3[+bGb1]{ } 29.Lb3*b4-b5[+bGb3] 30.Lb5*b7-b8[+bGb5] 31.Lb8*b5-b4[+bGb8] 32.Lb4*c4-d4[+bGb4]{ } 33.Ld4*g4-h4[+bGd4] 34.Lh4*d4-c4[+bGh4] 35.Lc4*b4-a4[+bGc4] 36.La4*b3-c2[+bGa4]{ } 37.Lc2*c4-c5[+bGc2] 38.Lc5*c2-c1[+bGc5] {=}

    This problem is not a length record, but contains a switchback of locust.

    SDP3 Vaclav Kotesovec, original
    white LRd4 black Gd6c5d5e5f5e4d3
    Rook-Locust - 7 Grasshoppers

    1.LRd4*e4-f4[+bGd4] 2.LRf4*d4-c4[+bGf4] 3.LRc4*c5-c6[+bGc4] 4.LRc6*d6-e6[+bGc6]{ } 5.LRe6*e5-e4[+bGe6] 6.LRe4*e6-e7[+bGe4] 7.LRe7*e4-e3[+bGe7] 8.LRe3*d3-c3[+bGe3]{ } 9.LRc3*c4-c5[+bGc3] 10.LRc5*d5-e5[+bGc5] 11.LRe5*f5-g5[+bGe5] 12.LRg5*e5-d5[+bGg5]{ } 13.LRd5*c5-b5[+bGd5] 14.LRb5*d5-e5[+bGb5] 15.LRe5*e3-e2[+bGe5] 16.LRe2*e5-e6[+bGe2]{ } 17.LRe6*c6-b6[+bGe6] 18.LRb6*b5-b4[+bGb6] 19.LRb4*f4-g4[+bGb4] 20.LRg4*g5-g6[+bGg4]{ } 21.LRg6*e6-d6[+bGg6] 22.LRd6*g6-h6[+bGd6] 23.LRh6*d6-c6[+bGh6] 24.LRc6*c3-c2[+bGc6]{ } 25.LRc2*c6-c7[+bGc2] 26.LRc7*e7-f7[+bGc7] 27.LRf7*c7-b7[+bGf7] 28.LRb7*b6-b5[+bGb7]{ } 29.LRb5*b4-b3[+bGb5] 30.LRb3*b5-b6[+bGb3] 31.LRb6*b7-b8[+bGb6] 32.LRb8*b6-b5[+bGb8]{ } 33.LRb5*b3-b2[+bGb5] 34.LRb2*c2-d2[+bGb2] 35.LRd2*e2-f2[+bGd2] 36.LRf2*d2-c2[+bGf2]{ } 37.LRc2*b2-a2[+bGc2] 38.LRa2*c2-d2[+bGa2] 39.LRd2*f2-g2[+bGd2] 40.LRg2*d2-c2[+bGg2]{ } 41.LRc2*g2-h2[+bGc2] 42.LRh2*h6-h7[+bGh2] 43.LRh7*h2-h1[+bGh7] 44.LRh1*h7-h8[+bGh1]{ } 45.LRh8*b8-a8[+bGh8] 46.LRa8*a2-a1[+bGa8] {=}

    At the beginning, all the pieces are grouped in the center. Progressively white Locust moves away from the group to finish its way on the corner a1.

    HP1 Vaclav Kotesovec, original
    white Lb1 black Gh7g6a5g4a2h2
    Locust - 6 Grasshoppers

    1.Gh7-h1 Lb1*g6-h7[+bGb1] 2.Gh1-a1 Lh7*h2-h1[+bGh7] 3.Ga1-a3 Lh1*b1-a1[+bGh1]{ } 4.Ga3*a1[+wLa3] La3*a5-a6[+bGa3] 5.Ga3-a7 La6*a7-a8[+bGa6] 6.Gh1-h8 La8*a6-a5[+bGa8]{ } 7.Ga2-a6 La5*a6-a7[+bGa5] 8.Gh8-h6 La7*a5-a4[+bGa7] 9.Ga1-a5 La4*a5-a6[+bGa4]{ } 10.Gh7-h5 La6*a4-a3[+bGa6] 11.Gh5-f3 La3*f3-g3[+bGa3] 12.Ga3-h3 Lg3*g4-g5[+bGg3]{ } 13.Gh3-h7 Lg5*g3-g2[+bGg5] 14.Ga8-h1 Lg2*g5-g6[+bGg2] 15.Gh1-f3 Lg6*g2-g1[+bGg6]{ } 16.Gh6-f6 Lg1*g6-g7[+bGg1] 17.Ga6-g6 Lg7*f6-e5[+bGg7] 18.Gg6-g8 Le5*g7-h8[+bGe5] {=}

    White Locust executes a four corners theme h1-a1-a8-h8 to reach the goal.

    HP2 Vaclav Kotesovec, original
    white Lc2 black Ga6a7c7b8d8e8f8g8
    Locust - 8 Grasshoppers

    1...Lc2*c7-c8[+bGc2] 2.Gf8-h8 Lc8*b8-a8[+bGc8] 3.Gd8-f8 La8*c8-d8[+bGa8]{ } 4.Ge8-c8 Ld8*c8-b8[+bGd8] 5.Ga7-a5 Lb8*d8-e8[+bGb8] 6.Gf8-d8 Le8*d8-c8[+bGe8]{ } 7.Ga6-a4 Lc8*e8-f8[+bGc8] 8.Gg8-e8 Lf8*e8-d8[+bGf8] 9.Ga4-d1 Ld8*f8-g8[+bGd8]{ } 10.Gd1-b3 Lg8*b3-a2[+bGg8] 11.Gc8-c1 La2*c2-d2[+bGa2] 12.Gc1-e3 Ld2*e3-f4[+bGd2]{ } 13.Gb8-g3 Lf4*g3-h2[+bGf4] 14.Ga8-e8 Lh2*f4-e5[+bGh2] 15.Gh8-d4 Le5*d4-c3[+bGe5]{ } 16.Gd8-d1 Lc3*d2-e1[+bGc3] 17.Ga5-f5 Le1*e5-e6[+bGe1] 18.Ge8-e5 Le6*e5-e4[+bGe6]{ } 19.Ge1-b4 Le4*e6-e7[+bGe4] 20.Ge4-a4 Le7*b4-a3[+bGe7] {=}

    Sebastien Luce commented: "The play is very slow at the beginning, exclusively on the eight rank and the a-file, then progressively the pieces move to the center.
    At the end, white Locust is taken in a 'sandwich of two Grasshoppers' on the a-file."

    HP3 Vaclav Kotesovec, original
    white LRd1 black Gf8g7b1
    Rook-Locust - 3 Grasshoppers

    1...LRd1*b1-a1[+bGd1] 2.Gf8-h6 LRa1*d1-e1[+bGa1] 3.Ga1-f1 LRe1*f1-g1[+bGe1]{ } 4.Gh6-f8 LRg1*e1-d1[+bGg1] 5.Gg1-c1 LRd1*c1-b1[+bGd1] 6.Gf8-h6 LRb1*d1-e1[+bGb1]{ } 7.Gh6-f8 LRe1*b1-a1[+bGe1] 8.Gf8-h6 LRa1*e1-f1[+bGa1] 9.Ga1-g1 LRf1*g1-h1[+bGf1]{ } 10.Gh6-f8 LRh1*f1-e1[+bGh1] 11.Gh1-d1 LRe1*d1-c1[+bGe1] 12.Gf8-h6 LRc1*e1-f1[+bGc1]{ } 13.Gh6-f8 LRf1*c1-b1[+bGf1] 14.Gf8-h6 LRb1*f1-g1[+bGb1] 15.Gh6-f8 LRg1*b1-a1[+bGg1]{ } 16.Gf8-h6 LRa1*g1-h1[+bGa1] 17.Ga1-h8 LRh1*h6-h7[+bGh1] 18.Gh8-f6 LRh7*g7-f7[+bGh7]{ } 19.Gh7-e7 LRf7*f6-f5[+bGf7] 20.Ge7-g7 LRf5*f7-f8[+bGf5] {=}

    Sebastien Luce commented: "Black Grasshoppers f8, g7 move back and forth to h6-f8, waiting white Locust going to h1 with a similar movement on the first rank. White Locust has to execute a double linear rundlauf a1-h1-a1-h1 to bring black Grasshopper on the corner a1 which can go on the opposite corner h8, allowing at last white Locust to play with the black trio and to reach a stalemate. My favourite problem of the article !"

    HP4 Vaclav Kotesovec, original
    white LRa1 black Gb1c1g4a6h6a7f7d8
    Rook-Locust - 8 Grasshoppers

    1.Ga7-g7 LRa1*a6-a7[+bGa1] 2.Gg7-g3 LRa7*f7-g7[+bGa7] 3.Gg4-g8 LRg7*g3-g2[+bGg7]{ } 4.Gg8-c8 LRg2*g7-g8[+bGg2] 5.Gd8-h8 LRg8*c8-b8[+bGg8] 6.Gh8-h5 LRb8*g8-h8[+bGb8]{ } 7.Gb1-d1 LRh8*b8-a8[+bGh8] 8.Gc1-e1 LRa8*a7-a6[+bGa8] 9.Ga8-a5 LRa6*a5-a4[+bGa6]{ } 10.Gd1-f1 LRa4*a6-a7[+bGa4] 11.Ge1-g1 LRa7*a4-a3[+bGa7] 12.Gf1-h1 LRa3*a7-a8[+bGa3]{ } 13.Gh1-f3 LRa8*a3-a2[+bGa8] 14.Gh5-e2 LRa2*e2-f2[+bGa2] 15.Gg2-e4 LRf2*f3-f4[+bGf2]{ } 16.Gg1-e3 LRf4*e4-d4[+bGf4] 17.Gf2-f5 LRd4*f4-g4[+bGd4] 18.Gh8-c3 LRg4*d4-c4[+bGg4]{ } 19.Gg4-e6 LRc4*c3-c2[+bGc4] 20.Gh6-d6 LRc2*c4-c5[+bGc2] 21.Ga2-f7 LRc5*f5-g5[+bGc5]{ } 22.Ge6-g8 LRg5*c5-b5[+bGg5] 23.Gg8-g4 LRb5*g5-h5[+bGb5] {=}

    C+, Alybadix 3 hours 45 minutes

    HP5 Vaclav Kotesovec, original
    white LBd3 black Ga5e5g1
    Bishop-Locust - 3 Grasshoppers

    1.Ga5-f5 LBd3*f5-g6[+bGd3] 2.Gg1-g7 LBg6*d3-c2[+bGg6] 3.Gg7-g5 LBc2*g6-h7[+bGc2]{ } 4.Gg5-d5 LBh7*c2-b1[+bGh7] 5.Gd5-f5 LBb1*f5-g6[+bGb1] 6.Gh7-f5 LBg6*f5-e4[+bGg6]{ } 7.Ge5-e3 LBe4*g6-h7[+bGe4] 8.Ge3-e5 LBh7*e4-d3[+bGh7] 9.Gb1-e4 LBd3*e4-f5[+bGd3]{ } 10.Ge5-g5 LBf5*d3-c2[+bGf5] 11.Gg5-e5 LBc2*f5-g6[+bGc2] 12.Gh7-f5 LBg6*f5-e4[+bGg6]{ } 13.Ge5-e3 LBe4*c2-b1[+bGe4] 14.Ge3-e5 LBb1*e4-f5[+bGb1] 15.Gg6-e4 LBf5*e4-d3[+bGf5]{ } 16.Ge5-g5 LBd3*f5-g6[+bGd3] 17.Gg5-g7 LBg6*d3-c2[+bGg6] 18.Gb1-d3 LBc2*d3-e4[+bGc2]{ } 19.Gg7-g5 LBe4*c2-b1[+bGe4] 20.Gg6-g4 LBb1*e4-f5[+bGb1] 21.Gg5-e5 LBf5*g4-h3[+bGf5]{ } 22.Ge5-g5 LBh3*f5-e6[+bGh3] 23.Gh3-d7 LBe6*d7-c8[+bGe6] {=}

    With the reduction of the power of the white piece, longer solutions in h=n can be obtained with a Bishop-Locust.
    Here we see successive linear rundlaufs h7-b1 by the Bishop-Locust before to finish on another part of the board in c8.

    HP6 Vaclav Kotesovec, original
    white LBc8 black Ga5b1b8f6f7h4h5h7
    Bishop-Locust - 8 Grasshoppers

    1.Gf7-f5 LBc8*f5-g4[+bGc8] 2.Gh5-f3 LBg4*f3-e2[+bGg4] 3.Gh4-f4 LBe2*g4-h5[+bGe2]{ } 4.Gc8-a8 LBh5*e2-d1[+bGh5] 5.Gf6-f3 LBd1*f3-g4[+bGd1] 6.Gh5-f3 LBg4*f3-e2[+bGg4]{ } 7.Ga8-a4 LBe2*g4-h5[+bGe2] 8.Ga4-g4 LBh5*g4-f3[+bGh5] 9.Gd1-a1 LBf3*e2-d1[+bGf3]{ } 10.Gf4-f2 LBd1*f3-g4[+bGd1] 11.Gh5-f3 LBg4*f3-e2[+bGg4] 12.Gb1-e1 LBe2*g4-h5[+bGe2]{ } 13.Gd1-f1 LBh5*e2-d1[+bGh5] 14.Gf1-f3 LBd1*f3-g4[+bGd1] 15.Gh5-f3 LBg4*f3-e2[+bGg4]{ } 16.Gd1-f1 LBe2*g4-h5[+bGe2] 17.Ge1-e3 LBh5*e2-d1[+bGh5] 18.Gf1-f3 LBd1*f3-g4[+bGd1]{ } 19.Gh5-f3 LBg4*f3-e2[+bGg4] 20.Gf2-d2 LBe2*g4-h5[+bGe2] 21.Gd1-d3 LBh5*e2-d1[+bGh5]{ } 22.Gd3-f3 LBd1*f3-g4[+bGd1] 23.Gh5-f3 LBg4*f3-e2[+bGg4] 24.Gd1-d3 LBe2*d3-c4[+bGe2]{ } 25.Ge2-b5 LBc4*b5-a6[+bGc4] 26.Ga5-a7 LBa6*c4-d3[+bGa6] 27.Ga6-e2 LBd3*e2-f1[+bGd3]{ } 28.Ga1-a8 LBf1*d3-c4[+bGf1] 29.Gf1-b5 LBc4*b5-a6[+bGc4] 30.Ga7-f2 LBa6*c4-d3[+bGa6]{ } 31.Gf2-c2 LBd3*c2-b1[+bGd3] 32.Ge3-c3 LBb1*d3-e4[+bGb1] 33.Ga8-f3 LBe4*f3-g2[+bGe4]{ } 34.Gd2-h2 LBg2*e4-d5[+bGg2] 35.Gh2-f2 LBd5*g2-h1[+bGd5] {=}

    Length record.

    Notation of the fairy pieces (Popeye compatible)
    G = Grasshopper
    L = Locust
    LR = Rook-Locust
    LB = Bishop-Locust

    For direct stalemate problems with Locust and pawns see the article by Jaroslav Štúò & Sébastien Luce: Locust Length Records, Bulletin 10/2016, p. 414-418.
    For definitions of fairy pieces see Fairy Glossary (section 3.6 Locust family) or Märchenschachlexikon (Locust = Heuschrecke)

    Acknowledgment. Thank you to Sebastien Luce for his help in the redaction.
    In addition, Sebastien dedicated the following original to me,
    with a comment: A "purely figurative problem" dedicated to the author of the article.

    Diagrams created with Py2Web