(;AB[pp]AB[pq]AB[qo]AB[nq]AB[mq]AB[mr]AB[no]AW[nr]AW[or]AW[pr]AW[qq]C[Black to play and kill White ]AP[goproblems]
(;B[rp];W[sr]C[Black attaches at 1 to restrict White's living space, then pulls back at 3. There is now no way for White to live.
]LB[rq:1]LB[rr:2]LB[rp:3];B[ns];W[os];B[qs];W[rs];B[qr]LB[sr:1]LB[ns:2]LB[os:3]LB[qs:4]LB[rs:5]LB[qr:6]C[It White descends at 1, Black hanes at 2, then makes the placement of 4. These moves exemplify two important principles of life-and-death problems: kill with a hane and take the vital point for making two eyes.
(;B[qp];W[qr]LB[rq:1]LB[rr:2]LB[qp:3]LB[qr:4]LB[rp:a]LB[sr:b]LB[sp:c]C[Amateurs often yield to the
temptation to atari at 3, but after 4 Black has
to defend at 'a', so White can live with 'b'. Better than this would be to play a ko with Black 'b', White 'a', Black 'c', but this is, of course, also a failure compared to the correct answer.
(;B[rr];W[rq];B[qr];W[rs];B[qs];W[sr];B[ss];W[sq]LB[rr:1]LB[rq:2]LB[qr:3]LB[rs:4]LB[qs:5]LB[sr:6]LB[ss:7]LB[sq:8]C[Black 1 does occupy the vital point for eye space, but when White counters with 2, Black finds that he can't capture him. There's no need to play such a difficult move when there's a simpler one available.