The question is whether to slide into White's eye space with a small-knight or large-knight move. The follow-up to both looks difficult, but you'll find things are simpler after the small-knight move. This problem was probably chosen because it often appears in actual games and because it's a 'clean' (that is, uncluttered)
shape
(;AW[rq]AW[qq]AW[pq]AW[oq]AW[nq]AB[rp]AB[pp]AB[qp]AB[op]AB[np]AB[mp]AB[mq]AB[mr]AB[rn]C[Black to play and kill White]AP[goproblems]
(;B[os];W[ps];B[ns]
(;W[or]LB[rs:a]LB[qr:b]LB[qs:c]LB[os:1]LB[ps:2]LB[ns:3]LB[or:4]C[The restrained move of 1 is the more powerful of the two obvious candidates. If White 2, Black calmly pulls back at 3. White 4 is the only move what happens now? The position after 4 would also make an excellent life-and-death problem. If Black 'a', White gets a ko with 'b'; if instead Black 'c', White attaches at 'a' and lives.]
(;B[rs];W[qr]C[];B[qs]C[After Black 1 to White 4, you might see the vital point at Black 5 first However, in this case, White makes eye shape with 6; even if Black attacks at 7, the best he can get is a koCHOICE]LB[os:1]LB[ps:2]LB[ns:3]LB[or:4]LB[rs:5]LB[qr:6]LB[qs:7])
(;B[qs];W[rs]C[CHOICE])
(;B[qr]
(;W[rr];B[sq];W[sr];B[rs]LB[qr:1]LB[rr:2]LB[sq:3]LB[sr:4]LB[rs:5]LB[qs:a]C[Black makes a direct attack on White's eye shape with 1. If White 2, Black 3 and 5 make a sanmoku-nakade (a three-point single eye). This works because White can't play in at 'a'. RIGHT])
(;W[rs];B[sr];W[sq];B[rr]LB[rs:1]LB[sr:2]LB[sq:3]LB[rr:4]C[White jumps to 1. Black counters with the placement at 2. After hite 3, Black connects at 4. This isn't a seki; it's a three-space big eye.RIGHT]))
(;B[sq];W[sr];B[qr];W[rs]LB[sq:1]LB[sr:2]LB[qr:3]LB[rs:4]C[Starting with the hane of 1 here (instead of the placement at 3) is a mistake. Now when Black plays 3, White lives with 4. CHOICE]))
(;W[rs]
(;B[sr];W[sq];B[pr]LB[qr:a]LB[os:1]LB[ps:2]LB[ns:3]LB[rs:4]LB[sr:5]LB[sq:6]LB[pr:7]C[After Black 1 and 3, White 4 is a desperate measure. Of course, Black 5 is the vital point: after White 6, playing atari at 7 kills White unconditionally. If Black gets flustered and plays 5 at 7, he lets White play 'a' and live.RIGHT])
(;B[pr];W[qr]C[CHOICE])))
(;B[ps]
(;W[nr];B[ns];W[os];B[or];W[pr]LB[ps:1]LB[nr:2]LB[ns:3]LB[os:4]LB[or:5]LB[pr:6]LB[qs:a]LB[ms:b]LB[rr:c]C[The large-knight move of 1 is wrong. White counters with 2 to 6. If Black connects at 4, White lives with White 'a', Black 'b', White 'c'. That means that Black has to fight a ko by extending to 'a' after White 6.]
(;B[os];W[qs]C[CHOICE];B[ms];W[rr]C[CHOICE]
(;B[sr];W[sq]C[CHOICE])
(;B[ss];W[sq]C[CHOICE]))
(;B[ms];W[rr];B[os];W[qs];B[sq];W[sr]C[CHOICE])
(;B[qs];W[os]C[koCHOICE]))
(;W[qs];B[os]LB[ps:1]LB[qs:2]LB[os:3]C[Wanting to enter just a little bit deeper is human nature and the slide to Black 1 is probably the first thing that comes to mind. In response, the attachment at 2 is too straightforward. After Black pulls back with 3, there isn't enough space for White to make life. White 2 is equally as bad a move as Black 1.CHOICE])))
