Penrose Puzzle

[Adam Hair]

The plan of white is simple to put the white king at d7 and trade knights at c7 when the last knight mate.

I believe black cannot prevent it.

I'm not convinced it's so easy. If black can trade/give away his bishops, he's stale-mated. In the initial position, all white's knights are trapped and will be captured once they move. Not a problem for the first one or two, but you still need to get that last knight into position.

you are probably right and I edited my post before seeing your reply.

3 knights are probably not enough and you need 4 for it.

I don't think that would work since all 4 knights would need to attack c7 at the moment when you want to start trading the first knight on c7, provided all 3 black bishop stay on the same diagonal b8-h2. You think of a sequence like Nc7+ - Bxc7 - Nxc7+ - Bxc7 - Nxc7+ - Bxc7 - Nxc7# if I understood you right (and there I also don't see the relevance of having a white king on d7). The problem of having 4 knights that attack c7 would be that one of them would need to be on a8 (the others on e8, e6, d5) but going to a8 would require passing c7 already which is impossible.

Wouldn't 3 knights be sufficient?

If it was only one bishop vs one knight, then White wins. Get the knight in position and then push the pawn to c7. If the bishop captures the knight off diagonal, push the pawn.

If it were 2 bishops vs 2 knights, move the knights into position and then push the pawn. Move the king so that if Black captures a knight before it is in position (d5, e6, or e8), then White can take the bishop. If this happens, then the position reduces to 1 bishop vs 1 knight.

The same procedure works (I think) for 3 bishops vs 3 knights.

I think that you are right and 3 knights are enough against 3 bishops.

The point is that with one knight against one bishop you put the king at c8 and only later play c7 Kb8 with the plan Ka8 c8=Q mate assuming black does not capture c7 and of course capturing c7 lead to Nxc7 mate.

I had missed the reason for moving the king until reading this response (c7 allows the Black king to slip out and threaten the pawn). That oversight is an example of why I am not good at chess and why I normally refrain from posting in this type of thread.

[peter]

Of course, Dann, I'd say it's a rather easy kind of fortress for the engines compared to really difficult ones.

Here 50 moves boundary is to be got into "sight" quickly with some Forward and kept in Hash in Backward easily too, if it's just big enough.

No matter with or without tbs

[IanO]

I wonder if there is some way to modify this position to give white an actual winning strategy, such as a king wander to a8 to support c7-c8=B#.

[Jouni]

Actually original article was 100% correct: white can even win. 1. c7 Bh4. 2. c8B mate .

[Arpad Rusz]

I have modified the original position:

[D]8/pP6/kpP3p1/brpPb1p1/1pP1PbP1/1P6/K5P1/8 w - - 0 1

White wins!

[peter]

I have modified the original position:

[D]8/pP6/kpP3p1/brpPb1p1/1pP1PbP1/1P6/K5P1/8 w - - 0 1

White wins!

Wow, Arpad!


8/pP6/kpP3p1/brpPb1p1/1pP1PbP1/1P6/K5P1/8 w - - 0 1

Analysis by Sting SF 7.3 64bit:

...
1.Kb1
-+ (-8.16 ++) Tiefe: 34 00:00:10 68819kN
1.d6
-+ (-7.97 ++) Tiefe: 34 00:00:14 112MN
...
1.d6
+- (96.47 ++) Tiefe: 34 00:00:20 170MN
...
1.d6 Lxd6 2.e5 Lh2 3.Kb1 Lf4 4.Kc2 Lb8 5.Kd3 Lbxe5 6.Ke4 Lb8 7.Kd5 Le3 8.Ke6 Lef4 9.Kd7 Lfc7 10.g3 Ld6 11.c7 Lbxc7 12.Kc6 Lxg3 13.cxb5#
+- (#13) Tiefe: 35 00:00:38 475MN
...

1.d6 Lxd6 2.e5 Lh2 3.Kb2 Lhxe5+ 4.Kc2 Lc7 5.Kd3 Lb2 6.Ke4 Lbe5 7.Kd5 Lg7 8.Ke6 Lce5 9.Kd7 Lc7 10.b8S+ Lxb8 11.c7 Kb7 12.c8D+ Ka8 13.Dc6#
+- (#13) Tiefe: 54 00:02:55 1304MN

Main branch SF fights quite a time with it.

[Arpad Rusz]

I have modified the original position:

[D]8/pP6/kpP3p1/brpPb1p1/1pP1PbP1/1P6/K5P1/8 w - - 0 1

White wins!

The solution is the following:

1. d6! (1. Kb1? Bd6! 2. e5 Bfxe5 3. Kc2 Bf4 =) 1... Bxd6 2. e5! Bfxe5 3. Kb1 Bb8 4. Kc2 Bf4 5. Kd3 Bfe5 6. Ke4 Bf4 7. Kd5 Bfe5 8. Ke6 Bf4 9. Kd7 Bfc7 10. g3! mutual zugzwang 10... Bxg3 11. c7! Bgxc7 (11... Kxb7 12. c8=Q+ Ka8 13. Qc6#) 12. Kc6 Bf4 13. cxb5#


In order to win, white has to sacrifice 4 pawns! Without the g2 pawn, the result is only a draw. The pawn is needed for a tempo move (see 10. g3!).

[Arpad Rusz]

Another related position:

[D]8/3p4/1p3k2/1Pp3p1/BRP1B1P1/KPp3P1/Pp4B1/8 w - - 0 1

Draw

[peter]

I have modified the original position:

[D]8/pP6/kpP3p1/brpPb1p1/1pP1PbP1/1P6/K5P1/8 w - - 0 1

White wins!

The solution is the following:

1. d6! (1. Kb1? Bd6! 2. e5 Bfxe5 3. Kc2 Bf4 =) 1... Bxd6 2. e5! Bfxe5 3. Kb1 Bb8 4. Kc2 Bf4 5. Kd3 Bfe5 6. Ke4 Bf4 7. Kd5 Bfe5 8. Ke6 Bf4 9. Kd7 Bfc7 10. g3! mutual zugzwang 10... Bxg3 11. c7! Bgxc7 (11... Kxb7 12. c8=Q+ Ka8 13. Qc6#) 12. Kc6 Bf4 13. cxb5#


In order to win, white has to sacrifice 4 pawns! Without the g2 pawn, the result is only a draw. The pawn is needed for a tempo move (see 10. g3!).

I'm really impressed, Arpad!
Even the MateFinder has its difficulties with it.
Beautiful Piece!

[Nordlandia]

Matefinder is updated (17 March)

http://chess.ultimaiq.net/stockfish.html