Here is the famous go problem Igo Hatsuyoron 120
Black to play and win
Source and Context
Designed for the training of the highest caliber students at the school. It was kept secret from all but a few of them, who studied the book under the direct supervision of the Inoue.
The problem above is number 120 from the collection, which has gained a reputation as the “Most Difficult Problem Ever”*. Despite several decades of research by many professionals, amateurs, and, most recently, AI-assisted analysis, this problem appears to still be unsolved, with “many classical solutions seemingly refuted and modern lines still not entirely certain” (ref: Jane Street Tech Blog, linked below).
Prior to the rise of strong AI, the state of the art (as of 2011) human research appears to be documented on this multi-lingual website: http://www.dgob.de/dgoz/trmdpe/
A Stunning Hanezeki
I cannot say that I even begin to understand this problem. However, I can say that one of the most profound features of this problem, which screams out at anyone that even casually scrolls through its main line, is this incredible hanezeki position:
Despite a huge 20-stone black chain being in atari, surprisingly neither black nor white should try to save or capture it, since making any move to do so would actually put them at a decisive disadvantage.
For more about hanezeki, see the Sensei’s library page or another forum thread where we discuss and analyze a related hanezeki that was composed by Harry Fearnley, as inspired by his study of Igo Hatsuyoron 120.
Recent AI Analysis
A difficulty with applying modern AI to the problem is that it was composed for Japanese rules with no komi (since komi was not widely adopted until centuries later). However, the problem’s requirement for very deep reading and understanding of large-scale, long-distance fights plays a larger role in leading all previous attempts of using AI to fail.
I recently found out from this reddit post and a LifeIn19x19 discussion thread that a custom trained version of KataGo has been applied to this problem, seeming to yield some promising and possibly novel results. The main announcement is on this site: