Gokyo Shumyo, Section 1, Problem 55 / Solution

Traditional Solution  

White forces with and (the order of which is important) then with threatens to make a second eye: Black can't make it false at the marked point, because White will push through at a and take two stones. So he plays , upon which White connects at .

Now at first sight, the shape is one of a dead group: a three point eye, and a false eye at the top.

Continuation  

Surprisingly enough, White plays first and then , capturing two Black strings at once. This makes miai of replaying under the stones!! For reference ...

Continuation  

Each of Black's eye-reducing moves (throw-in at and nakade at ) is possible only after White's capture. So White delays the capture of three stones and set up to capture both Black strings in one move. Then and are miai; Black can play only one of them, allowing White to make life by playing the other. This double capture technique is called nichō-nuki in Japanese.

Alternative solution at a  

In fact, the other atari similarly works too.

Failure at 9  

At , if White plays instead of a, Black answers at to keep White down to one eye. If next White captures two stones at a, he throws in at . White should capture simultaneously to make miai of Black's answers. The order of a and is important.

Failure at 7  

If White plays at here (instead of connecting at ) Black captures at and the miai are destroyed.

Failure at 5  

White has now one big eye almost filled with three stones. There is no threat in a.

Failure at 3  

If White changes the order of and , Black can answer at and make it ko with .

Order of 3 and 5 - variation at 4  

In the main line, White hasn't yet exchanged b for , so when she plays atari at , and captures, makes miai of a and b.

Variation - order of 1 and 3  

Suppose is not answered at a; then makes life.

Variation - order of 1 and 3  

But Black can answer at , then at as in this diagram. Next, White comes one move too late: after , a and b are miai.