Challenge

[Fermin Serrano]

This problem is mate in 6!!!.


FEN: n1N3br/2p1Bpkr/1pP2R1b/pP1p1PpR/Pp4P1/1P6/1K1P4/8 w - - 0

I have not found any engine that can solve it. I thought strong engines would fine the mate in a few seconds. Craft need more than two minutes in my machine to find a very looooong sequence for mate, but the mate in 6 is hidden to it.

why?

[Teemu Pudas]

Why?

Nullmove. There are five zugzwangs, so it's unsolvable (or takes something like depth 30 with verification searches) for engines that don't consider the number of legal moves when deciding whether to do it.

Edit: Fruit 2.1 with verification reduction = 3 gets it in 18 iterations - 2 minutes, 25 seconds on my computer.

[Reinhard Scharnagl]

Having found a simple Zugzwang avoiding method inside of alpha beta with nullmove heuristic SMIRF MS-174d-0 gives:

Code: Select all

00:01.1 (08.01=) +M~006 1.Rh1 (Kc1) d4 2.Ra1 d3 3.Ra3 bxa3+ 4.Ka1 a2 5.Ba3 Kxf6 6.Bb2#
00:00.9 (08.01+) +3.742 1.Rh1 (Kc1) d4 2.Re1 d3 3.Nd6 cxd6 4.Rxd6 f6 5.Bxf6+ Kf8 6.Rd8+ Kf7 7.Bxh8 Rxh8 8.Rxa8 Kg7
00:00.6 (07.04=) +3.299 1.Rh1 (Kc1) d4 2.Re1 d3 3.Nd6 cxd6 4.Rxd6 f6 5.Bxf6+ Kf8 6.Rd8+ Kf7 7.Bxh8 Rxh8 8.Rxa8 Kg7
00:00.5 (07.02=) +1.297 1.Kc1 (Rh3) d4 2.Rh3 d3 3.Bd8 Kf8 4.Rxd3 Kg7 5.Re3 Kf8 6.Be7+ Ke8
00:00.3 (07.01+) +1.295 1.Rh3 (Kc1) d4 2.Kc1 d3 3.Bd8 Kf8 4.Rxd3 Kg7 5.Re3 Kf8 6.Be7+ Ke8
00:00.2 (06.02=) +1.074 1.Rh3 (Kc1) d4 2.Kc1 d3 3.Bd8 Kf8 4.Rxd3 Kg7 5.Re3 Kf8 6.Be7+ Ke8
00:00.2 (06.02+) +1.076 1.Kc1 (Rh3) d4 2.Rh3 d3 3.Bd8 Kf8 4.Rxd3 Kg7 5.Re3 Kf8 6.Be7+ Ke8
00:00.0 (05.02=) +0.271 1.Rh3 (Kc1) d4 2.Kc1 d3 3.Bd8 Kf8 4.Be7+ Kg7 5.Bd8 Kf8 6.Be7+ Kg7 7.Bd8 Kf8 8.Be7+ Kg7
00:00.0 (02.13=) +0.020 1.Kc1 (d4) d4 2.Bf8+

P.S.: Correction: that method is not Zugzwang avoiding, but Zugzwang neutral - it avoids Zugzwang problems.