The helpmates and stalemates with n pieces of the same value

Pomocné maty a paty s více kameny stejných hodnot

(Václav Kotěšovec, 15.4.2021)

1) White pieces of the same value

Jaký je minimální počet kamenů stejných hodnot, se kterými (bez vlastního krále) existuje matová (resp. patová) pozice se samotným soupeřovým králem ?
Jaký je nejdelší pomocný mat s tímto materiálem ?

What is the minimum number of pieces of the same value with which (without his own king, against bare king) there exists a checkmate position ?
What is the longest helpmate with this material?

S ortodoxními kameny je tato úloha triviální. Mnohem zajímavější jsou přeskakující kameny.

With orthodox pieces, this problem is trivial. Hoppers are much more interesting.

Notation of the fairy pieces
  G = Grasshopper
RH = Rookhopper
BH = Bishophopper
NH = Nightriderhopper
KA = Kangaroo


Zatímco úlohy s jedním řešením se cvrčky a věžovými cvrčky jsou poměrně nezajímavé (pro srovnání viz třeba PDB P1378116 se 4 řešeními!), úlohy se střelcovými, tátošovými cvrčky a klokany dosahují značných délek a i hra je zajímavá.

While helpmates with one solution with grasshoppers and rookhoppers are relatively uninteresting (for comparison, see PDB P1378116 with 4 solutions!), problems with bishophoppers, nightriderhoppers and kangaroos reach considerable lengths and also the play is more interesting.



S1 Vaclav Kotesovec, original
white BHa8 BHb1 BHc1 BHc8 BHd8 BHf8 BHh1 black Ka1
h#19
7 Bishophoppers
C+

1.Ka1-b2 BHc1-a3 2.Kb2-c2 BHb1-d3 3.Kc2-b2 BHa3-c1{ } 4.Kb2-c2 BHd3-b1 5.Kc2-d3 BHb1-e4 6.Kd3-e3 BHc1-f4{ } 7.Ke3-d4 BHh1-d5 8.Kd4-e5 BHf4-d6 9.Ke5-f5 BHe4-g6{ } 10.Kf5-e6 BHf8-c5 11.Ke6-d7 BHc8-e6 12.Kd7-c7 BHd6-b8{ } 13.Kc7-b6 BHc5-a7 14.Kb6-c5 BHa7-d4 15.Kc5-d6 BHb8-e5{ } 16.Kd6-e7 BHd8-f6 17.Ke7-f8 BHa8-e4 18.Kf8-g8 BHd5-f7+{ } 19.Kg8-h8 BHe5-g7#


S2 Vaclav Kotesovec, original
white BHc1 BHc8 BHd3 BHd8 BHh2 BHh4 black Ka1
h=18
6 Bishophoppers
C+

1.Ka1-b2 BHc1-a3 2.Kb2-c2 BHd3-b1 3.Kc2-b2 BHa3-c1{ } 4.Kb2-c2 BHb1-d3 5.Kc2-d2 BHc1-e3 6.Kd2-c2 BHd3-b1{ } 7.Kc2-d3 BHb1-e4 8.Kd3-d4 BHe3-c5 9.Kd4-d5 BHe4-c6{ } 10.Kd5-e6 BHc8-f5 11.Ke6-f6 BHh4-e7 + 12.Kf6-g6 BHf5-h7{ } 13.Kg6-f5 BHh7-e4 14.Kf5-e6 BHc5-f8 15.Ke6-d7 BHf8-d6{ } 16.Kd7-c8 BHe7-c5 17.Kc8-b8 BHh2-c7 + 18.Kb8-a8 BHd8-b6{=}



S3 Vaclav Kotesovec, original
white NHa2 NHb2 NHc1 NHc2 NHd6 NHe8 NHg2 black Kb1
h#17
7 Nightriderhoppers
C+

1.Kb1-a1 NHe8-c4 2.Ka1-b1 NHg2-a5 3.Kb1-a1 NHa5-e3+{ } 4.Ka1-b1 NHc2-g4 5.Kb1-a1 NHc4-g2 6.Ka1-b1 NHb2-e8{ } 7.Kb1-b2 NHe8-h2 8.Kb2-c3 NHa2-e4 9.Kc3-d4 NHh2-b5{ } 10.Kd4-d3 NHc1-e5 11.Kd3-d4 NHb5-f3 12.Kd4-d3 NHe5-g1{ } 13.Kd3-e2 NHg1-c3 14.Ke2-d2 NHf3-b1 15.Kd2-c1 NHb1-d5{ } 16.Kc1-b2 NHg2-c4+ 17.Kb2-a1 NHg4-c2#
S4 Vaclav Kotesovec, original
white NHb8 NHd8 NHe3 NHh2 NHh8 black Kb1
h=15
5 Nightriderhoppers
C+

1.Kb1-c2 NHe3-a1 2.Kc2-b3 NHa1-c5 3.Kb3-b4 NHd8-a2{ } 4.Kb4-b3 NHc5-a1 5.Kb3-b4 NHa2-c6 6.Kb4-b3 NHa1-c5{ } 7.Kb3-c4 NHb8-d4 8.Kc4-d5 NHh2-b5 9.Kd5-e5 NHc6-g4{ } 10.Ke5-f4 NHh8-e2 11.Kf4-e5 NHe2-c6 12.Ke5-d6 NHb5-f7{ } 13.Kd6-c7 NHg4-a7 14.Kc7-b7 NHa7-e5 15.Kb7-a8 NHf7-d3{=}

S5 Vaclav Kotesovec, original
white KAa1 KAa3 KAa8 KAb6 KAc1 KAg7 KAg8 KAh2 black Kf8
h#25
0.1.1...
8 Kangaroos
C+

1... KAa8-h8 2.Kf8-e8 KAh8-d8 3.Ke8-f8 KAg8-c8{ } 4.Kf8-g8 KAc8-h8 5.Kg8-h7 KAh8-h1 6.Kh7-h6 KAh1-h7{ } 7.Kh6-h5 KAh7-h1 8.Kh5-h4 KAh1-h5 9.Kh4-h3 KAh2-h6{ } 10.Kh3-h2 KAh6-h1 11.Kh2-g1 KAh1-b1 12.Kg1-f1 KAb1-g1{ } 13.Kf1-f2 KAg1-a7 14.Kf2-e3 KAa1-a8 15.Ke3-d4 KAa7-e3{ } 16.Kd4-d3 KAa3-f3 17.Kd3-e4 KAa8-g2 18.Ke4-f4 KAc1-g5{ } 19.Kf4-g4 KAh5-e2 20.Kg4-f4 KAg5-d2 21.Kf4-g3 KAg7-g1{ } 22.Kg3-f2 KAg1-d4+ 23.Kf2-f1 KAd8-d1 24.Kf1-g1 KAb6-f2+{ } 25.Kg1-h1 KAd1-d5#


S6 Vaclav Kotesovec, original
white KAa1 KAa7 KAb7 KAf1 KAg8 KAh5 black Kd1
h=33
6 Kangaroos
C+

1.Kd1-c1 KAa1-g1 2.Kc1-b1 KAg1-a1 3.Kb1-a2 KAa1-a8{ } 4.Ka2-a3 KAa8-a2 5.Ka3-a4 KAa2-a8 6.Ka4-a5 KAa8-a4{ } 7.Ka5-a6 KAa7-a3 8.Ka6-a7 KAa3-a8 9.Ka7-b8 KAa8-h8{ } 10.Kb8-c8 KAh8-b8 11.Kc8-d8 KAb8-h8 12.Kd8-e8 KAh8-d8{ } 13.Ke8-f8 KAg8-c8 14.Kf8-g8 KAc8-h8 15.Kg8-h7 KAh8-h4{ } 16.Kh7-h6 KAh4-h7 17.Kh6-g7 KAh7-a7 18.Kg7-f7 KAa7-g7{ } 19.Kf7-e7 KAb7-h7 20.Ke7-f7 KAh7-e7 21.Kf7-f6 KAd8-g5{ } 22.Kf6-e5 KAh5-d5 23.Ke5-f5 KAg5-c5 24.Kf5-e5 KAc5-f5{ } 25.Ke5-f6 KAf1-f7 26.Kf6-e5 KAd5-g5 27.Ke5-d5 KAg5-c5{ } 28.Kd5-e5 KAf5-b5 29.Ke5-d6 KAc5-f8 30.Kd6-c5 KAf8-b4{ } 31.Kc5-c6 KAa4-d7 32.Kc6-b7 KAf7-c7 + 33.Kb7-a8 KAe7-b7{=}


2) Black pieces of the same value

Přejděme teď k opačné situaci. Bílý má jen jeden kámen (bez krále), černý má krále a několik kamenů stejných hodnot.
Jaký je minimální počet těchto kamenů aby byl možný pomocný mat s tímto materiálem a jakou má největší délku ?

Většinou existují matové nebo patové pozice i s menším počtem černých kamenů, neexistuje k nim však poslední tah. To vyžaduje přidání dalšího černého kamene.

Let us now turn to the opposite situation. White has only one piece (without a king), black has a king and several pieces of the same value.
What is the minimum number of these pieces such that to exists a helpmate with this material and what is its greatest length?

There are usually mating or stalemate positions with a smaller number of black pieces, but there is no last move. This requires the addition of next black piece.




S7 Vaclav Kotesovec, original
white NHg8 black Kf8 Ga2b1d1g1h2
h#19
1 Nightriderhopper
5 Grasshoppers
C+

1.Kf8-e7 NHg8-c6 2.Gd1-h1 NHc6-g8 3.Ke7-f6 NHg8-e4 4.Gh1-d5 NHe4-g8 5.Ga2-e6 NHg8-e4{ } 6.Gb1-f5 NHe4-g8 7.Gf5-c5 NHg8-e4 8.Gg1-b6 NHe4-g8 9.Gc5-e5 NHg8-e4 10.Ge5-e7 NHe4-g8{ } 11.Kf6-e5 NHg8-c6 12.Ge6-e4 NHc6-g8 13.Ke5-d6 NHg8-c6 14.Kd6-c7 NHc6-g8 15.Gh2-b8 NHg8-c6{ } 16.Kc7-b7 NHc6-g8 17.Kb7-a8 NHg8-c6 18.Gd5-b7 NHc6-g8 19.Ge7-a7 NHg8-d2#






S8 Vaclav Kotesovec, original
white NHe8 black Kg6 NHc8 NHh8 NHa7 NHg7 NHh3 NHe2
h#42
1+6 Nightriderhoppers
C+

1.Kg6-f6 NHe8-g4 2.Kf6-e5 NHg4-c6 3.NHe2-b8 NHc6-g4 4.Ke5-f6 NHg4-e8 5.NHb8-h5 NHe8-g4{ } 6.Kf6-e5 NHg4-c6 7.Ke5-d4 NHc6-e2 8.Kd4-c3 NHe2-a4 9.NHa7-d1 NHa4-e2 10.Kc3-d4 NHe2-c6{ } 11.Kd4-e5 NHc6-g4 12.Ke5-f6 NHg4-e8 13.NHh5-d7 NHe8-g4 14.Kf6-e5 NHg4-c6 15.Ke5-d4 NHc6-e2{ } 16.Kd4-c3 NHe2-a4 17.NHd1-b5 NHa4-e2 18.Kc3-d4 NHe2-c6 19.Kd4-e5 NHc6-g4 20.NHd7-f3 NHg4-c6{ } 21.NHb5-h2 NHc6-g4 22.NHh2-f6 NHg4-e8 23.Ke5-e4 NHe8-g4 24.NHc8-f2 NHg4-e8 25.Ke4-d5 NHe8-g4{ } 26.NHh3-b6 NHg4-e8 27.Kd5-c4 NHe8-b2 28.NHb6-d2 NHb2-d6 29.NHh8-b5 NHd6-b2 30.NHb5-h2 NHb2-d6{ } 31.NHh2-d4 NHd6-b2 32.NHf3-b5 NHb2-d6 33.NHb5-f7 NHd6-h8 34.Kc4-d3 NHh8-d6 35.NHf2-b4 NHd6-h8{ } 36.Kd3-e4 NHh8-d6 37.Ke4-f5 NHd6-h4 38.Kf5-g6 NHh4-b1 39.Kg6-h7 NHb1-f3 40.Kh7-h8 NHf3-b1{ } 41.NHb4-h7 NHb1-f3 42.NHd2-g8 NHf3-b5#


S9 Vaclav Kotesovec, original
white NHc8 black Kb5 KAa8c3e2f8h5
h#65
1 Nightriderhopper
5 Kangaroos
C+

1.Kb5-b6 NHc8-a4 2.Kb6-c5 NHa4-e6 3.Kc5-d4 NHe6-c2 4.Kd4-e3 NHc2-g4 5.KAh5-d1 NHg4-c2{ } 6.Ke3-d4 NHc2-e6 7.Kd4-c5 NHe6-a4 8.Kc5-b6 NHa4-c8 9.KAa8-g8 NHc8-a4 10.Kb6-c5 NHa4-e6{ } 11.Kc5-d4 NHe6-c2 12.Kd4-e3 NHc2-g4 13.KAd1-h5 NHg4-c2 14.Ke3-d4 NHc2-e6 15.Kd4-c5 NHe6-a4{ } 16.Kc5-b6 NHa4-c8 17.KAg8-b8 NHc8-a4 18.Kb6-c5 NHa4-e6 19.Kc5-d4 NHe6-c2 20.Kd4-e3 NHc2-g4{ } 21.KAh5-d1 NHg4-c2 22.Ke3-d4 NHc2-e6 23.Kd4-c5 NHe6-a4 24.Kc5-b6 NHa4-c8 25.KAf8-a8 NHc8-a4{ } 26.Kb6-c5 NHa4-e6 27.Kc5-d4 NHe6-c2 28.Kd4-e3 NHc2-g4 29.KAd1-h5 NHg4-c2 30.Ke3-d4 NHc2-e6{ } 31.Kd4-c5 NHe6-a4 32.Kc5-b6 NHa4-c8 33.KAa8-d8 NHc8-a4 34.Kb6-c5 NHa4-e6 35.Kc5-d4 NHe6-c2{ } 36.Kd4-e3 NHc2-g4 37.KAh5-d1 NHg4-c2 38.Ke3-d4 NHc2-e6 39.Kd4-c5 NHe6-a4 40.Kc5-b6 NHa4-c8{ } 41.KAb8-e8 NHc8-a4 42.Kb6-c5 NHa4-e6 43.Kc5-d4 NHe6-c2 44.Kd4-e3 NHc2-g4 45.KAe8-e1 NHg4-c2{ } 46.KAe1-e4 NHc2-g4 47.KAe2-e5 NHg4-c6 48.Ke3-d4 NHc6-g4 49.Kd4-c5 NHg4-c6 50.KAc3-c7 NHc6-g4{ } 51.Kc5-d6 NHg4-c6 52.Kd6-e7 NHc6-g8 53.Ke7-d6 NHg8-d2 54.KAd1-d7 NHd2-f6 55.KAe5-b8 NHf6-d2{ } 56.Kd6-d5 NHd2-f6 57.KAd8-d4 NHf6-d2 58.Kd5-c4 NHd2-b6 59.KAe4-b4 NHb6-f8 60.Kc4-b5 NHf8-b6{ } 61.KAb4-b7 NHb6-f8 62.Kb5-a6 NHf8-b6 63.Ka6-a7 NHb6-f8 64.Ka7-a8 NHf8-c2 65.KAd7-a7 NHc2-e6# { Longest helpmate without fairy conditions of all times!}



S10 Vaclav Kotesovec, original
white KAa8 black Ka1 KAa3 KAb7 KAd2 KAf5 KAg1 KAh3
h#56
1+6 Kangaroos
C+

1.Ka1-a2 KAa8-a1 2.Ka2-b1 KAa1-h1 3.Kb1-c1 KAh1-b1 4.Kc1-d1 KAb1-h1 5.Kd1-e1 KAh1-d1{ } 6.Ke1-f1 KAd1-h1 7.Kf1-g2 KAh1-a8 8.Kg2-f3 KAa8-g2 9.Kf3-e2 KAg2-c2 10.Ke2-d3 KAc2-g6{ } 11.Kd3-c2 KAg6-b1 12.Kc2-b3 KAb1-b8 13.Kb3-b4 KAb8-b3 14.Kb4-b5 KAb3-b8 15.Kb5-b6 KAb8-b5{ } 16.Kb6-c5 KAb5-g5 17.Kc5-d5 KAg5-c5 18.Kd5-e5 KAc5-g5 19.Ke5-f4 KAg5-c1 20.Kf4-g5 KAc1-h6{ } 21.Kg5-h5 KAh6-h2 22.Kh5-h6 KAh2-h7 23.Kh6-g7 KAh7-a7 24.Kg7-f7 KAa7-g7 25.Kf7-e7 KAg7-a7{ } 26.Ke7-d7 KAa7-e7 27.KAh3-c8 KAe7-a7 28.Kd7-c7 KAa7-d7 29.KAc8-g4 KAd7-h3 30.Kc7-d6 KAh3-e6{ } 31.Kd6-e5 KAe6-h3 32.Ke5-f4 KAh3-e6 33.Kf4-g3 KAe6-h3 34.KAg1-g5 KAh3-e6 35.Kg3-f4 KAe6-h3{ } 36.KAd2-h6 KAh3-e6 37.KAh6-e3 KAe6-h3 38.Kf4-f3 KAh3-d3 39.Kf3-e4 KAd3-g6 40.KAg4-g7 KAg6-d3{ } 41.KAa3-f3 KAd3-g3 42.Ke4-f4 KAg3-d3 43.Kf4-g4 KAd3-g3 44.KAe3-h3 KAg3-g6 45.Kg4-g3 KAg6-g2{ } 46.KAg5-g1 KAg2-a8 47.Kg3-f4 KAa8-g2 48.Kf4-e5 KAg2-a8 49.Ke5-e6 KAa8-g2 50.KAh3-d7 KAg2-a8{ } 51.KAf5-c8 KAa8-g2 52.Ke6-f7 KAg2-a8 53.KAd7-h7 KAa8-g2 54.Kf7-g8 KAg2-a8 55.Kg8-h8 KAa8-g2{ } 56.KAg1-g8 KAg2-a8# { Switchback of the white kangaroo}






S11 Vaclav Kotesovec, original
white Ga1 black Kh1 KAa4a5e8
h=20
1 Grasshopper
3 Kangaroos
C+

1.Kh1-g1 Ga1-h1 2.Kg1-f1 Gh1-e1 3.Kf1-e2 Ge1-e3 4.Ke2-d2 Ge3-c1 5.Kd2-c3 Gc1-c4{ } 6.Kc3-d4 Gc4-e4 7.KAa4-f4 Ge4-c4 8.Kd4-d3 Gc4-e2 9.Kd3-e4 Ge2-e5 10.KAe8-e3 Ge5-g3{ } 11.Ke4-d5 Gg3-e5 12.KAa5-f5 Ge5-c5 13.KAf5-b5 Gc5-f2 14.Kd5-c4 Gf2-d4 15.KAf4-b4 Gd4-f2{ } 16.Kc4-b3 Gf2-d4 17.KAb5-b2 Gd4-a1 18.KAb4-b1 Ga1-c1 19.Kb3-a2 Gc1-f4 20.Ka2-a1 Gf4-d2{=}



S12 Vaclav Kotesovec, original
white NHc2 black Ka3 NHf8g4h3h5
h=31
1+4 Nightriderhoppers
C+

1.Ka3-b4 NHc2-a6 2.Kb4-c5 NHa6-e4 3.Kc5-d6 NHe4-c8 4.Kd6-e7 NHc8-g6 5.NHf8-h4 NHg6-c8{ } 6.Ke7-d6 NHc8-e4 7.Kd6-c5 NHe4-a6 8.Kc5-b4 NHa6-c2 9.NHg4-a1 NHc2-a6 10.Kb4-c5 NHa6-e4{ } 11.NHa1-d7 NHe4-a6 12.NHh5-b8 NHa6-e4 13.NHb8-f6 NHe4-g8 14.Kc5-d5 NHg8-e4 15.NHh3-b6 NHe4-g8{ } 16.Kd5-d6 NHg8-e4 17.NHh4-b7 NHe4-c8 18.Kd6-e5 NHc8-a4 19.NHd7-f3 NHa4-c8 20.Ke5-e4 NHc8-f2{ } 21.Ke4-d3 NHf2-b4 22.NHb7-e1 NHb4-h7 23.NHe1-g5 NHh7-d5 24.NHb6-f4 NHd5-h7 25.NHf4-b2 NHh7-d5{ } 26.Kd3-c3 NHd5-b1 27.NHg5-a2 NHb1-h4 28.Kc3-c2 NHh4-d2 29.Kc2-b1 NHd2-h4 30.Kb1-a1 NHh4-d2{ } 31.NHf3-b1 NHd2-g8{=}
S13 Vaclav Kotesovec, original
white NHd2 black Kg5 KAa8b5f2f8
h=40
1 Nightriderhopper
4 Kangaroos
C+

1.Kg5-f6 NHd2-g8 2.KAa8-h8 NHg8-e4 3.KAf8-f1 NHe4-g8 4.KAf1-f7 NHg8-e4 5.KAf2-f8 NHe4-g8{ } 6.KAh8-e8 NHg8-e4 7.KAf8-f5 NHe4-g8 8.Kf6-e7 NHg8-c6 9.KAe8-a4 NHc6-g8 10.Ke7-f6 NHg8-e4{ } 11.KAf5-f8 NHe4-g8 12.Kf6-e7 NHg8-c6 13.KAa4-d7 NHc6-g8 14.KAf7-c7 NHg8-c6 15.KAb5-e8 NHc6-g8{ } 16.KAe8-h8 NHg8-c6 17.KAc7-f7 NHc6-g8 18.Ke7-f6 NHg8-e4 19.KAf8-f5 NHe4-g8 20.Kf6-e7 NHg8-c6{ } 21.KAd7-g7 NHc6-g8 22.Ke7-f6 NHg8-e4 23.KAh8-e5 NHe4-g8 24.Kf6-e7 NHg8-c6 25.Ke7-f6 NHc6-g4{ } 26.Kf6-g5 NHg4-c6 27.Kg5-f4 NHc6-g4 28.KAf7-f3 NHg4-c6 29.KAf5-f2 NHc6-g4 30.Kf4-e4 NHg4-c6{ } 31.KAf3-b7 NHc6-g4 32.Ke4-d4 NHg4-c6 33.KAg7-c3 NHc6-e2 34.KAe5-b2 NHe2-a4 35.Kd4-c4 NHa4-e2{ } 36.Kc4-b3 NHe2-a4 37.KAb7-b1 NHa4-e2 38.Kb3-a2 NHe2-a4 39.Ka2-a1 NHa4-e2 40.KAf2-a2 NHe2-a4{=}



S14 Vaclav Kotesovec, original
white KAg8 black Kh1 KAc2d1e3g3h5
h=52
1+5 Kangaroos
C+

1.Kh1-g2 KAg8-g1 2.Kg2-f1 KAg1-c1 3.Kf1-g1 KAc1-h1 4.Kg1-h2 KAh1-h6 5.Kh2-h3 KAh6-h2{ } 6.Kh3-h4 KAh2-h6 7.Kh4-g5 KAh6-d2 8.Kg5-f4 KAd2-g5 9.Kf4-g4 KAg5-g2 10.Kg4-g5 KAg2-g6{ } 11.Kg5-f5 KAg6-b1 12.Kf5-e4 KAb1-f5 13.Ke4-d3 KAf5-b1 14.KAg3-c3 KAb1-e4 15.KAe3-b3 KAe4-b1{ } 16.Kd3-e4 KAb1-f5 17.KAd1-a4 KAf5-b1 18.Ke4-f5 KAb1-g6 19.KAa4-d1 KAg6-b1 20.Kf5-g6 KAb1-h7{ } 21.Kg6-h6 KAh7-h4 22.Kh6-h7 KAh4-h8 23.Kh7-g7 KAh8-b2 24.KAd1-a4 KAb2-h8 25.Kg7-h6 KAh8-h4{ } 26.KAa4-d1 KAh4-h7 27.Kh6-g6 KAh7-b1 28.Kg6-f5 KAb1-g6 29.Kf5-e4 KAg6-b1 30.Ke4-d3 KAb1-e4{ } 31.KAb3-e3 KAe4-b1 32.KAc3-f3 KAb1-e4 33.Kd3-e2 KAe4-e1 34.KAd1-g4 KAe1-e4 35.Ke2-d3 KAe4-b1{ } 36.KAh5-e2 KAb1-e4 37.KAf3-c3 KAe4-e1 38.Kd3-d4 KAe1-e4 39.Kd4-e5 KAe4-e1 40.Ke5-f5 KAe1-e4{ } 41.KAc2-g6 KAe4-h7 42.Kf5-e4 KAh7-d3 43.Ke4-f3 KAd3-g3 44.KAg6-g2 KAg3-d3 45.KAe3-b3 KAd3-a3{ } 46.Kf3-e3 KAa3-d3 47.KAc3-f3 KAd3-g3 48.Ke3-f2 KAg3-a3 49.KAe2-h2 KAa3-g3 50.Kf2-g1 KAg3-a3{ } 51.Kg1-h1 KAa3-g3 52.KAg4-g1 KAg3-a3{= Switchback of the black king}



Diagrams created with Py2Web