(;AB[rd][rf][qf][pf][pe][pc][pd][od][nd][md][lb][qj][pi][oh][ng][mg][kg][if][he]
[ic][jc][kd][lc]AW[le][jd][je][ke][me][nf][og][ph][qh][qi][rj][ld][mc][nc][oc][pb]
[re][qe][qd][qc][rc][ql]C[Black first to live. This problem contains many steps, but all necessary and can be calculated.

Note\: Problem extracted from #118 in Igo Hatsuyoron
]
AP[MultiGo:4.2.1]SZ[19]CA[gb2312]MULTIGOGM[1]
;B[of]C[Black cut is the only way out];W[pg];B[qb];W[ob];B[rb]
(;W[sb]C[If white does not capture]
(;B[sd]C[T16 is the correct move at extending black's liberty]
(;W[qa]
(;B[se]C[T15 is a more complicated variation for black];W[ra];B[rh];W[ri];B[ne]
;W[mf];B[sh];W[sf]
(;B[rg]C[Black 17 connects to extend its liberties]
(;W[kc];B[kb];W[si];B[rk];W[qk];B[lf]C[Black kills white's group])
(;W[jg]
(;B[jf]C[19 to cut white from escaping is not a good choice];W[lg];B[lh];W[kf];B[kh]
;W[mh];B[nh];W[mi]
(;B[oi];W[oj];B[pj];W[ok]C[Ko, black is in danger])
(;B[nj];W[ki]C[妙手]
(;B[jh];W[ni];B[oi];W[oj]C[Ko, black in danger])
(;B[li];W[mj];B[nk];W[mk];B[nl];W[jh]C[Ko, bad for black])))
(;B[jh]C[19 to prevent white from escaping rather than cutting white, black is in a better shape outside]
;W[lg];B[lh];W[kf];B[kh];W[mh];B[nh];W[mi];B[oi];W[oj];B[nj];W[ig];B[jf];W[kc];B[kb]
;W[li];B[ok];W[hg];B[hh];W[ih];B[ji];W[ii];B[jj];W[hd];B[id];W[ie];B[hf];W[ge];B[gf]
;W[ff];B[gg]C[White dies, not a ko. Better for black])))
(;B[sg]C[If black captures at 17];W[qg]
(;B[lf];W[kc];B[kb];W[rg];B[rk];W[qk];B[jf];W[sc]C[Ko is not good enough for black])
(;B[rg];W[rk]C[Another ko, not good for black])))
(;B[ne]C[If black chooses 9 instead of playing on the side at T15];W[mf];B[ri];W[rh]
;B[sf];W[kc];B[kb];W[sg];B[lf];W[rg];B[jf]C[Black kills white with more liberties. Thus 9 is simpler than T15]))
(;W[se];B[ne];W[mf];B[sf];W[sc];B[rh];W[ri];B[sh]C[Black lives]))
(;B[sf]C[Black 7 does not help];W[rg];B[sd];W[qa];B[ne];W[mf];B[lf];W[kc];B[kb]
;W[ra];B[ri];W[si];B[jf];W[sg]C[Black dies]))
(;W[sd]C[If white chooses to capture];B[sb];W[qa];B[ra];W[pa];B[sf];W[sc];B[rh]
;W[ri];B[ne];W[mf];B[sh]C[Black lives on the side using white corner's sente.]))