Answer



Dia. 1. Correct		 Dia. 1. The diagonal connection
White must defend with the diagonal connection of 1. This is not the way White would normally defend the marked stone; he would want to connect at 'a'. For this reason, it is a hard move to see.



Dia. 2. Capturing a stone		 Dia. 2. Sacrificing three stones
The efficacy of White 1 in Dia. 1 can be appreciated by seeing the continuation. Black tries to live by making an eye in the corner with the atari of 2 and threatening to capture two stones. But White plays a brilliant move with 3, increasing the sacrifice to three stones. After Black captures with 4 —



Dia. 3. Black's group is dead		 Dia. 3. Capturing a stone
Black recaptures a stone with 5 and, surprisingly, Black ends up with a false eye at 'a'. With only one eye in the corner, Black's group is dead.



Dia. 4. Sacrificing three stones		 Dia. 4. Capturing a stone
Instead of the atari of 2 in Dia 2, the atari from below with Black 2 also fails. Again White sacrifices three stones with 3. After Black captures with 4 —



Dia. 5. A dead three space eye		 Dia. 5. A dead three-space eye
Black ends up with a dead three-space eye. White makes a placement on the key point of 5 and Black's group is dead.



Dia. 6. Capturing a stone		 Dia. 6. A ko
Immediately turning at 1 is a mistake. Black will atari at 'a' and live. However, if Black mistakenly ataries with 2, White will atari at 3. When Black captures with 4, the result is a ko.



Dia. 6. Capturing a stone		 Dia. 6. The solid connection
The solid connection of White 1 fails. With the atari of 2, Black makes an eye in the corner and captures two stones without any bad aji.


Sacrificing stones often leads to sequences that are hard to read out, especially after some stones are captured and the opponent makes a recapture. This can transform the entire nature of a position. When such positions arise in games, a player can't analyze them by moving the stones around on the board. Instead, he must analyze the position in his head. And this is how one should solve life-and-death problems: visualize the position in your head and solve them there.

A few years ago I wrote an essay on this topic, Increasing Your Concentration and Powers of Analysis through Visualization. Perhaps some of my readers will find this essay useful.