Gokyo Shumyo, Section 1, Problem 3 / Solution

Main line  

After , which makes an eye at the circled point, a and b are miai for life. Instead of , c also lives, but allows white to seal off the right side: see below.

Because there are two possible solutions, this problem may be called unsound if you use a specific definition for sound/unsound problems.

2 and 3 are miai (i)  

After , Black has real eyes at the circled points.

2 and 3 are miai (ii)  

It seems as if creates a false eye, but the capture of three stones on the first line with results in a real eye.

2 and 3 are miai (ii continued)  

Even if White throws in at , Black lives with .

Variation  

White's best endgame followup is to capture a Black stone with . Then or a makes a second eye. However, if Black doesn't respond, White a kills the group. After , black has just over 3 1/2 points in the corner (later, either side may play b in gote).

Wrong (i)  

at the other 1-2 point is wrong. With , Black is dead. Even if Black is allowed two moves in a row, he can't live.

Wrong (ii)  

When Black plays here, White kills with . ( at is an inferior way to kill, because after Black and White a, Black gets some concrete threats at c.)

Wrong (iii)  

Connecting with Black , as shown here, is also wrong. and leave a and b as miai for the kill.

Another way to live  

Making the eye as large as possible, with here, also lives.

Difference ( at )  

To this way of living, White can seal the right side in sente. is necessary to avoid ko: see bent four in the corner. This is the reason why the main line solution is usually preferred.

Alternative followup  

Early in the game, if there are other big moves remaining on the board, KataGo actually prefers here rather than the main line. The reason is that in the diagram above won't be sente if black is in a good position to fight the ko. Instead, white has this and as forcing moves. Black has only 3 points of corner territory, compared to nearly 4 points in the main line; however, black can push out at b in sente. So in some contexts, this choice of is actually more profitable than the main line.