: (A 57; B 60)
Black's group at upper right does not have two eyes yet. However, the sequence starts in the lower right corner. The other sources agree on the first few moves, but do not give reasons for them.

In general terms, Black could get two eyes for his upper right group - if he intends to do so, there is no way that White can prevent this, but it would be at the minimum cost of letting White live in the lower right corner (and possibly losing the Black group in the lower right), thereby losing the game for Black by (at least) a few points.

In our opinion, the meaning of , as a kikashi, is primarily to prevent White from living in this corner; Black's threat to connect with his top right group is secondary only.

: (A 61)
It seems very likely that at (or at , or ) will simply lead to a change in the order of moves. We have not yet made detailed investigations for other variations for . However, it seems to us that these will fail.

: (A 62)
This move finally prevents easy life for White in the corner; other Black moves will again fail here.

In principle, White is now forced either to connect her -group to the outside, or to capture Black's -group. Ideally, she will manage this task while not letting Black's top right group connect to the bottom one, and while keeping sente to play on the left side first.

However, this problem is so designed that White will only gain a partial success. White's -group will indeed surround Black's -group, but will itself also get surrounded by Black's groups, so that a temporary seki will emerge in this area.

: (6 63)
White tries to connect out.

at (or ) is very likely simply to lead to a change in the order of moves.

(A 64)
Other alternatives, like , fail here. Some alternatives were very tricky, and time consuming, for us to refute.

: (11 67)
Cutting at does not work for White. Black's bottom group will get sufficient liberties to kill White's group in the corner, thus capturing White's stones above, including her -group.

:
Both Black's -group, and White's -group, are now isolated.

: (17 71)
Black can no longer escape, so he starts to spoil the shape of White's enclosing group, and to reduce its liberties. We think that it is technically best to cut first, because Black now - in principle - has the option to get two eyes for his group in the upper right.
It is possible for Black to play at first. This move can be found in the professional solutions ( 715); it will result in a change in the order of moves.

: (18 103)
Black would be able to secure a second eye for his top right group by capturing two White stones, starting with the atari at , instead. However, this will not be sufficient to win the game.

:
Until Cheng Xiaoliu 6p used this move in 2010 [LIT. 9], the other professional commentaries said that Black must not throw-in a second time at . A discussion on this topic can also be found in this book ( 914).

In principle, Black gains an advantage of one point by using this second throw-in, making up for the prisoner that he had lost before the problem starts ( 778).

at (White will answer at ) will now have no effect other than losing an important liberty of the group at the right edge, and a potential ko-threat as well, and so should not be played so early.

:
Black must prevent a White move on this point that would result in an eye for White's group, so destroying the temporary seki on the right.

: (23 105)
Black cannot play at , instead. White will answer at , isolating the resulting temporary seki involving the entire lower right corner from the rest of the board. Black's top right group cannot get two eyes, so White will win the game with ease.

With the exchange of , so early in the game Black would only lose a potential ko-threat, and a liberty of his large group above, unnecessarily.

: (25 107; 26 109)
White can play neither at , nor at , instead. Black would be able to capture White's group in the lower right corner, so dissolving the hanezeki, and winning the game.

: (A 110)

If Black plays at here, he can neither escape White's encirclement nor kill White's group at the bottom.

(26 112)
Black could secure life for his lower group by capturing two White stones with a move at . But White will do the same for her group in the corner by playing at . Black's top right group cannot get two eyes, so White will win the game.

: (A 113)
Black cannot capture White's three stones with . His group has one liberty too few to win the resulting semeai on the lower edge.

: (29 115)
White cannot give atari at . Black will either capture at or give atari on his own (at ). Black's group will get two eyes.

Similarly, later White cannot give atari with (at ), or (at ).

: (B; C 58ah)
Black continues with further lengthening the hanezeki's tail.

KataGo (2021i) likes to reduce White's upper right corner, starting with the push at , as early as possible.
Thereafter, Black's guzumi at is also played "early".
This "early" guzumi enables White to initiate a variation of Our Solution, which does not contain the Main Semeai, but looks much more like a "real" game.
Please note that in the subvariation the Hanezeki Exchange has already been played by Black.

: (35 117)
White cannot block at . Again, Black can either capture at or take White's point with a move at to win the fight in the corner.

: (A 118)
This move is an important kikashi, for securing some points of territory.

: (39 119)
White must answer Black's kikashi locally. She cannot succeed by putting the hanezeki's tail into atari by playing at , instead. As usual, Black will force her to capture the tail, and Black will win.

: (40 121)
Playing this move at does not work. Black's group cannot break out and connect. White's group on the bottom edge can be cut off, but will easily get two eyes.

:
White cannot give atari at . The same principle applies as with .

: (44 123)
White cannot play geta at , instead. Black would have one liberty too many, and could now capture at , and win the fight with the White group in the bottom right corner, and so the game.

Similarly, she cannot play geta with her moves from to .

: (45 124)
White cannot block Black's path at . Black would push through at , and then connect out or force White to capture the hanezeki's tail in order to save her group on the lower edge. This would lead to the loss of all the White stones at lower right.

:
The same principle as with applies, should White play at now.

: (53 125)
If White plays at instead, Black's centre group gets an additional outside liberty with a move at , and thereafter Black captures White's corner.

: (55 126)
White cannot stop Black's escape with . Black cuts at and wins.

: (56 127)
Black cannot play at , instead. His top right group will lose a liberty, and thereafter lose the semeai with White's group on the left edge.

Black might also consider playing the hiki of later, to reach a ko, but his move at will not prove helpful then, too.

:
The same principle as with applies, should White play at now.

: (61 131)
White cannot block at , because it will be Black who wins the resulting ko.

: (64 133)
It is not correct for Black to separate White's groups with . However, an interesting, and new, seki variation could then arise.

Black might also consider playing the hiki of later, because his stone at may have hurt White's shape on the upper edge.

: (B 165)
If White plays at instead, she can obtain another ko. However, as with mistakenly playing at , she will be as unable to win the ko.

(Referenced by 730f)

: (C 166)
After long research, we think that it is technically best to insert some kikashi in the top right corner right now, just before the all decisive moment of the game (this is the choice between the guzumi of , and the start of the Crosscut Sequence with ). However, Black should not start with playing the hasami-tsuke at first.
The professional solution continues immediately with the Crosscut Sequence ( 716), starting with a move at , and has some kikashi in the top right corner later.

: (A 169)
It does not profit White to answer at , instead.

(B 175)
However, trying to take a liberty from Black's group with a move at , does not work at all, because Black will easily get two eyes, so winning the game.

(C 176)
Neither does it work for White to take one of Black's potential eyes below.

:
This hasami-tsuke was found by Harry Fearnley and is further explained by us ( 790). It gives Black quite a large territorial advantage in one of the forthcoming main variations of the problem, and is even playable with the professional solution ( 738); but there without effect.

: (A 178)
Again, pre-empting one of Black's potential eyes below, with a move at , will not help White.

: (A 179)
And for the third time, destroying the miai of and , instead, does not profit White.

The Main Path of our solution will continue later ( 197).