Hardest chess problem. Stockfish 12 can’t solve it.

Hello, I attach the following problem that Stockfish 12 couldn’t solve while running for 20 mins on my PC and reaching depth 34.

All chess engines are content with 1.Qd6+ Kg8 2.gxh7+ Kh8 3.Bxa5, which hardly yields more than a draw. There is, however, a very clear and forced win with a dramatic second move that is thrilling to see. 1.Qc8! Kg8 2.Bc7!! This is the star move. Why it's hard for a computer to find 2.Bc7!! is because White has for at least 16 ply only a pawn and a bishop against black's queen, knight and two pawns. But Black is in zugzwang! 2...Qxc8 [2...Nxc7 3.gxf7+] 3.gxf7+ Kh8 [3...Kf8 4.Bd6#] 4.Be5. White is threatening to move his king and discover check and mate. 4...Qc5 5.Bb2 Nc7. Black has the white king contained, but cannot afford to move either the queen or the knight for fear of mate. 6.Ba1 a4 7.Bb2 a3 8.Ba1 a2 9.Bb2 a1Q 10.Bxa1 and now Black is in deadly zugzwang - he must move either the queen or the knight. 10...Nd5+ 11.Ke6+ Nc3 12.Bxc3+ Qxc3 13.f8Q# 1-0.

A long long time ago it used to be that engines looked at all the moves n-ply deep and used an evaluation function to evaluate the child nodes. This is a naive approach and is not a good use of engine resources as not all moves are equally good. Why waste resources exploring moves that are obviously bad? Modern engines have a policy network which determines how good a move is based on a static evaluation of the board and allocates resources accordingly. While this significantly improves the engine strength in the average case, there can be cases such as these where the right move receives a low score by the policy network and too few resources are allocated to exploring it. 

I had Stockfish 12 evaluate the position and it only saw the mate in 13 from the initial position after just over 30 minutes at a depth of 98/26.

n2Bqk2/5p1p/Q4KP1/p7/8/8/8/8 w - - 0 1

Analysis by Stockfish 150920:

1.Qc8 Kg8 2.Bc7 Qxc8 3.gxf7+ Kh8 4.Be5 Qc5 5.Bb2 Nc7 6.Ba1 a4 7.Bb2 a3 8.Ba1 a2 9.Bb2 a1Q 10.Bxa1 Nd5+ 11.Ke6+ Nc3 12.Bxc3+ Qxc3 13.f8Q#
+- (#13) Depth: 78/26 00:00:27 109MN
(gambit-man, 16.09.2020)

Wow. Can't say I'd find that one on my own!

This is why I use 3-line PV analysis combined with 'group moves'. In this case, I set SF 12 to only consider queen moves, and it found the mate in less than two minutes at depth 64. When analyzing positions, I always sort by group moves to find candidates of each type of piece or pawn move.

I've come across this puzzle very interesting and thought provoking 

Cool! Lol if stockfish can't solve it, I wouldn't know where to start lol.

stockfish can solve it... in less than 30 seconds.  see post #4. and in less than 2 minutes in multi-PV mode. see post #6

nope, i just set my engine up correctly...

Beautiful puzzles !

interesting....

I analysed it, if Black instead took the bishop its a draw

Well technically he did 'see' the solutions. :-P

WOW Thats god level.

No, instead of Kb1, he could've taken the bishop on a1

hmm your right, seems stockfish cant solve this!

In 3-line PV mode, the latest SF dev build will randomly solve it at different time intervals on my Ryzen 7 2700X. I had one iteration take 3 minutes to solve it, and clearing memory, another iteration solved it in 5 seconds flat.

ShashChess 15.1 gets this relatively quickly

A fine puzzle.