The Hardest Puzzle Ever Composed

No engine can calculate brute force at depth 43 or even close to that. It will use reductions based on probable outcomes which are pretty useless in this particular endgame. Every time an evaluation score is generated other than 99, 0 or -99, the engine admits it may be overlooking critical things - which is effectively through the greatest part of every chess game.

Much worse for the engines than games are artificial compositions. These are set up to demonstrate the power of moves and strategies that are ineffective in common chess games (like underpromotions) and will therefore consistently be misestimated by "game engines" like stockfish. That the engines solve so many of them anyway is due to (a) the tremendous brute force capability that modern engines do have (b) the multi-phased construction of many studies which allows the engines to solve it in "parts"; each part constitutes a tangible success in comparison to alternatives in that part and is within the brute force horizon.This is no different from how they analyze games.

The particular study by Gijs van Breukelen has no clear phases and black seems on top from the first to the prelast move. To the engines this is like crossing an ocean to find "the promised land"  on the other side while the stars are clouded and no other navigation tools are availabe. It can send out its probes but few reach far enough to be helpful in plotting a winning course. And those that do have strayed too far to find a way back "home". 

Note: "Brute force" is used in a relative sense here since modern engines no longer calculate all the moves in a graph branch. But they will find all the relevant moves and variations within a limited scope by generating enriched random move sequences to locate desirable endpoints (winning positions), and then zoom in on the candidates. Think of it as a fishing net. Nearby the mazes are small and no fish escapes but at a distance they are wider and even a whale might get through. A real world example of the same ideas at work was the "battle of Midway" during WWII where the U.S. aircraft carriers long remained invisible to the japanese reconnaissance net by staying at a considerable distance.

Fascinating... thanks!

I don't see the engines having any problem with this puzzle. The few first moves are as the solution shows. Then Stockfish finds a mate in 11 if it forks the queen and the king. So it just plays 4...Kg4 instead!

At that position White has an advantage. So the puzzle isn't totally refuted but with best play the solution isn't correct. Any human would do the fork and capture the Queen, let's be serious

"Best play" does not exist, except to separate 1-0, 1/2-1/2 and 0-1. Within each result group all moves are equally "best".

There are conventions in compositions regarding the selections of dualfree lines to determine which lines are part of the solutions, which lines are part of the tries and which lines are neither. That includes directions for the counterplay.

If 4 ... Kg4 does not draw in the final analysis, then it is not a relevant part of the solution even when it maximizes the distance to mate. It is not "the best" move because absolutely all black moves are equally "best" - they all lose.

Only if 4... Kg4 turns out to deliver a draw, there is an argument to declare the study incorrect!

Almost all discussions on "best" moves are based on the perception that we live in the Skynet world, the bots have taken over and we just follow orders. I can assure you the engines and tablebases don't have a clue about the gradations by which humans appreciate solution and try lines. And our judgement on these matters is certainly "best".

I would say "best play" exists and matters in direct mate problems. Of course the problem here is a study. I just mention it because I've noticed many commenters don't seem to be aware of the distinction--they're all just "puzzles".

You are right. More accurate would have been to state is that "best play only separates the moves that achieve the desired goal and those that don't". This is even more true in games than in puzzles where it only applies to the 'defense'.

I think that this is the hardest puzzle white to move and win

Slightly more interesting with the wK on e2. Checkmate in 4 but still close to being the easiest puzzle ever composed.

For hardest puzzle one candidate would be the one Arisktotle explained where White has to castle to prove that Black can't castle. Or maybe that would be weirdest puzzle.

This puzzle is on YouTube.Just type beautiful endgames and hit the search button...

The Chesspuzzler has this puzzle here.. I think is great

https://www.youtube.com/watch?v=DTOpiIbUu0A&t=27s

this is so easy

I know exactly what the answer is and I have probably seen it on youtube

If you go to youtube, search "hardest checkmate in one puzzle in the world", and skip to the answer, it will be an enpasant or whatever that is called.