Problem Solution

So, here’s the problem.

Black to play and live.

Now, in the game in which this situation was encountered, my opponent played the following move:

I responded as follows:

Black responded in an attempt to live, and at first blush, it looks like it should work. However:

This move is called a “throw-in”. At first, it seems odd. The white stone will be captured, of course. But watch what happens when black captures:

Now the outside black stone is in atari, and black must fill:

But, now black’s stones are in atari, and white can kill. Clearly, black’s first move was incorrect.

The following would be the correct move:

At this point, white would like to try and kill the group. However, watch what happens:

Black now has two eyes, and lives! Similarly, any other move by white would produce the same result. Thus, this move by black makes the group unconditionally alive.