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Black to capture the white stones. Based on a problem from Basic Life and Death Encyclopedia by Cho Chikun (基本死活事典, 1996).
Solution (textual): c1 threatens capture and creates the basic "straight three" shape. If white captures with a1, black plays again at c1 to prevent the formation of two eyes.
Black to live. Based on a problem from "Brilliancies from Go Classics" by Hayashi Genbi (碁経衆妙, 1812).
Solution (textual): The vital point is the point of symmetry (a1). A simple descent at a4 or d1 results in the dead "bent four in the corner" shape.
Black to kill. Based on a problem from "Gateway to All Marvels" by Yan Defu and Yan Tianzhang (玄玄棋經, 1349).
Solution (textual): a2 kills. If white resists with a3, black pushes with b2. After c2, d1, d2, f1, white cannot prevent the connection due to shortage of liberties. If white attempts to make shape with d1, black prevents the eye with c2, b2, d2, c1, d2, c2, f1.