YuriyStepanovich:
Black C1 and kills white group. White G3 - B F1 - W G2 - B C1 and kills white group. Result White is dead.

Incognito:
I agree with jenjen comment, and would suggest to change the title for the following : "no eye versus small eye or one eye versus one eye depending on who plays first"

jen.jen:
In the specific situation when black has two outside liberties and white has no outside liberties, wouldn't black simply sacrifice his three stones to take ten stones and kill white? The correct answer here says "unsettled".