This is probably the most analyzed chess puzzle of all time - certainly on chess.com. When you look back at dozens of topics declaring "the hardest puzzle engines can't solve" you will inevitably find the one - this one. However, it is obsolete news. Modern engines do solve it - which is not the same as stating that your engine can solve it. They run it on supercomputers or a network of parallel processors. And not for 5 minuten but for hours or days if required. Theorists need to solve a problem just once and can afford the investment to make the next step in science.
VERY HARD puzzle for Chess Engines (feb 2022)

Yea, it's rather how a few engines can detect it early on. Implying that they clearly have properly set some detection (this is too generalized but yea).
From a human perspective, you won't let engine run for days in a gameplay hehe (or in tournaments)
Nice, i didn't know this one is well known.

There is also one of the most challenging chess puzzles comes from the famous endgame study by Nikita Pliskov. In this puzzle, the position appears deceptively simple, with White having a queen and a pawn, while Black only has a king and a few scattered pawns. At first glance, White seems to be in a winning position, but the puzzle requires careful calculation to find the precise sequence of moves. The key to solving it lies in understanding the concept of "opposition" and "king activity." It’s not just about pushing the pawn or using the queen aggressively; rather, it's about using both the king and queen in harmony to restrict the opponent's king and pawns while gradually advancing the own pawn to promote.
What makes this puzzle particularly hard is that it challenges the solver's ability to think ahead and to manage multiple threats simultaneously. White’s queen must avoid the traps set by Black’s advancing pawns, all while keeping the enemy king under tight control. There’s also the added difficulty of timing the pawn promotion, as the opponent's king can create immediate threats if the pawn is advanced too early. The solution requires several moves of calculation to ensure that Black’s pawns do not manage to either promote or create a deadly passed pawn.
The difficulty of the puzzle is amplified by the need for precision in the final moves. Often, puzzles like this one present multiple possible paths to victory, but only one precise solution leads to a checkmate or forced resignation. As with many hard chess puzzles, the answer doesn’t come from brute force but from understanding key principles like zugzwang, piece coordination, and the concept of underpromotion. The moment when the solver realizes the solution can feel like an epiphany, offering not just a win, but also a deeper understanding of advanced chess endgame strategies.
Most of the engines will think black is winning. Only 3 of the many engines i tried correctly detect white advantage here. Which is pretty impressive.
Those engines are:
Crystal 4 251221 (Stockfish clone)
Gull 3.0.1 (old engine)
ShashChess 20.2 (default, it also finds it in capablanca and petrosian mode)
Source (original site that i found it on), with some explanations: https://lichess.org/study/dfFkhY31
Note: i haven't tried every single engine there is, hehe.
I also didn't analyze for a long time, it's pretty clear at start. BUT some other engines might discover white advantage later on.