This problem follows the basic principle of life-and-death: reduce the opponent's eye space, then play at the vital point. Actually there are two solutions to this
problem, but that makes it no less instructive.
(;AB[pp]AB[oo]AB[rp]AB[ro]AB[oq]AB[nq]AB[mq]AB[mr]AW[nr]AW[or]AW[pq]AW[qq]AW[rq]C[Black to play and kill White]AP[goproblems]
(;B[ns]
(;W[ps]
(;B[sq];W[sr];B[rs]
(;W[qs];B[ms];W[rr];B[pr]LB[ns:1]LB[ps:2]LB[sq:3]LB[sr:4]LB[rs:5]LB[qs:6]LB[ms:7]LB[rr:8]LB[pr:9]LB[qr:a]C[The hane of 1 is obvious. Black further reduces White's eye space with 3, then makes the placement at the vital point of 5. These two moves are a combination faithful to the principle mentioned above. If White tries to make two eyes with 6, Black is able to destroy the second eye with 7 and 9. This is another important technique in life-and-death problems. Even if White plays 6 at 8 or at 'a', Black still connects at 7. RIGHT];W[qr];B[os]C[RIGHT])
(;W[rr];B[ms];W[qs];B[pr];W[qr];B[os]C[RIGHT])
(;W[qr];B[ms];W[os];B[qs]C[RIGHT]))
(;B[rs];W[sq];B[rr];W[qr];B[ms]LB[ns:1]LB[ps:2]LB[rs:3]LB[sq:4]LB[rr:5]LB[qr:6]LB[ms:7]C[Black can also kill White by making a placement at 3 immediately. If White 4, Black plays 5 and 7. However, the previous sequence is more faithful to the basics and more efficient. RIGHT])
(;B[qr];W[rr];B[sq];W[sr]LB[ns:1]LB[ps:2]LB[qr:3]LB[rr:4]LB[sq:5]LB[sr:6]C[Attacking White's eye shape prematurely with 3 is a crude move. This lets White live with 4 and 6. CHOICE])
(;B[rr];W[sr];B[qr];W[rs]LB[ns:1]LB[ps:2]LB[rr:3]LB[sr:4]LB[qr:5]LB[rs:6]LB[pr:a]LB[os:b]C[The attachment at 2 is another crude move. White lives with 4 and 6. Note that if White plays 2 at 'a', Black kills him simply by crawling at'b'. CHOICE]))
(;W[pr];B[os]C[RIGHT];W[rs];B[sr];W[sq];B[rr];W[ps];B[qr]C[RIGHT]))
(;B[rs];W[rr])
(;B[pr];W[qr];B[rs];W[ps];B[ns];W[rr])
(;B[sq];W[sr]
(;B[rr];W[sp])
(;B[pr];W[ps])
(;B[ps];W[pr])))