Players who have mastered the basics will solve this problem at a glance, but for others it's easy to play a crude move and help White live. The important thing is not to confuse this shape with the one in which White has an extra liberty open (at the marked stone) — that leads to a different result. The problem with the liberty open is a more difficult one, suitably for high-dan players.
(;AW[rq]AW[rp]AW[qq]AW[oq]AW[or]AB[nr]AB[nq]AB[np]AB[op]AB[pp]AB[qp]AB[ro]AB[qn]C[Black to play and kill White]AP[goproblems]
(;B[os]
(;W[pr];B[sp]LB[os:1]LB[pr:2]LB[sp:3]C[The two hanes of 1 and 3 kill White. This problem is a model illustration of the proverb, 'death lies in the hane'. Anyone with an elementary knowledge of life-and-death problems knows that White doesn't have enough space to live after 3; if you don't, you should spend some time with a life-and-death primer. RIGHT])
(;W[qs]LB[os:1]LB[qs:2]C[Regarding the position after Black's hane, White can think of several ways to defend himself. Of course, no matter what he plays, he can t avoid dying, but Black needs to know all of the variations. For example, how should Black respond to White 2?]
(;B[sp]
(;W[sr];B[rs]LB[os:1]LB[qs:2]LB[sp:3]LB[sr:4]LB[rs:5]C[You have to know how to kill White if he answers at 2. Once again, a simple hane does the trick. If White tries to confuse Black with 4, Black 5 will finish him off. RIGHT];W[rr]
(;B[pr]C[RIGHT])
(;B[pq];W[pr];B[ns]C[RIGHT]))
(;W[pq];B[ps];W[pr];B[rr]C[RIGHT]))
(;B[pr];W[pq];B[ps];W[qr];B[ns];W[sr]LB[pr:1]LB[pq:2]LB[ps:3]LB[qr:4]LB[ns:5]LB[sr:6]C[Playing atari at 1 is crass. White connects at 2 and now has managed to get a living shape. Black has to connect at 3, so with 4 and 6 White just manages to live.CHOICE])
(;B[rr];W[sp]
(;B[sr]C[RIGHT])
(;B[qr]C[RIGHT]))))
(;B[pq];W[pr];B[os];W[qs]LB[pq:1]LB[pr:2]LB[os:3]LB[qs:4]C[Pushing at Black 1 is also vulgar After White 2, the hane is correct in this position, but when White plays the open connection at 4, there is no longer any way to kill him. Additionally, continuing from this position, we have the following variation.]
(;B[ns];W[sr]
(;B[qr];W[rr];B[ps];W[sp]LB[pq:1]LB[pr:2]LB[os:3]LB[qs:4]LB[ns:5]LB[sr:6]LB[qr:7]LB[rr:8]LB[ps:9]LB[sp:10]C[Pushing down at 1 is a crude move. The result after 3 is to help White make eye shape. The best Black can do now is to capture three stones after 10. If Black plays 7 at 10, White lives with 'a'.]LB[rs:a])
(;B[rs];W[sp]C[CHOICE]))
(;B[sr];W[rr];B[ns];W[ss];B[ps];W[sq]LB[sr:1]LB[rr:2]LB[ns:3]LB[ss:4]LB[ps:5]LB[sq:6]LB[qr:a]LB[rs:b]C[Black's placement at 1 is a way to continue to harass the white group. If white 2, connecting along the bottom at 3 is powerful, but after White 4 and White 5, White captures at 6 and is alive. If White connects at 'a' instead of 6, Black captures at 'b', and since White cannot atari at 6, it's a ko.CHOICE]))
(;B[pr];W[pq];B[os];W[qr];B[ps];W[qs];B[ns];W[sr]LB[pr:1]LB[pq:2]LB[os:3]LB[qr:4]LB[ps:5]LB[qs:6]LB[ns:7]LB[sr:8]C[Black 1 is even cruder. It's easy for White to live. The belly attachment at Black 1 is also a vulgar play. When White connects at 2, even if Black links underneath at 3, White 4 and 6 are sente; with the diagonal move at 8, White is alive.CHOICE]))