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With hanging connections facing each other, white is forbidden to recapture at 1 after black captures at 2. White is required to play elsewhere with 3 (known as a ko threat). If black answers 3 at 4, then white can recapture at 1 with 5. This is known
as a 'Ko Fight'. However, if black ignores white 3 and plays black 4 at 1, the ko fight ends. Otherwise the ko fight continues.
Black is also forbidden to play at 5 because that will fill up the last liberty of the black group. Some rules do allow this kind of suicide moves.
Likewise, black is not allowed to play at 6 for the same reason above, except when capturing the white stones. However, in this case, black must first fill in at a first.