(;AB[pa]AB[qa]AB[oa]AB[ob]AB[qb]AB[qc]AB[qd]AB[pd]AB[od]AB[nd]AB[ne]AB[nf]AB[mf]AB[of]AB[pf]AB[re]AB[sd]AB[lg]AB[kh]AB[jh]AB[hg]AB[if]AB[je]AB[jd]AB[jc]AB[jb]AB[kd]AB[mh]AB[mi]AB[li]AB[mk]AB[ml]AB[nl]AB[ol]AB[gg]AB[gj]AW[ig]AW[jg]AW[jf]AW[ke]AW[lf]AW[me]AW[md]AW[ld]AW[kc]AW[kb]AW[lb]AW[mc]AW[nc]AW[oc]AW[pc]AW[pb]AW[nb]AW[na]AW[oe]AW[pe]AW[qe]AW[qf]AW[rf]AW[pg]AW[og]AW[ng]AW[mg]AW[nh]AW[ni]AW[nj]AW[nk]AW[ok]AW[pj]AB[ql]AP[goproblems]
(;B[qg]
(;W[rg]
(;B[qh];W[rh]
(;B[qi];W[ri]
(;B[qj];W[qk]
(;B[rj];W[rk]C[3 to 4, you'll lose the battle of liberties.])
(;B[rk];W[pk]
(;B[rj]C[2 dead White groups, right on the mark.RIGHT])
(;B[rl];W[rj])
(;B[pl];W[rj]))
(;B[pl];W[rj]
(;B[rk];W[pk])
(;B[pk];W[rk])))
(;B[rj];W[qj]))
(;B[ri];W[qi]))
(;B[kf];W[kg]TR[lg]TR[qg]C[The ko will offer White a lifeline when the R13 cut goes sour...]))
(;W[qh];B[rg]C[White's better defense. Next, if White ignores L14 Black might start the ko there without damaging the side's options.RIGHT]))
(;B[ih];W[qk]C[White sacrifies 4 to save many.])
(;B[kf]
(;W[qk]C[White protects the side in sente (assuming Black takes at M15 next).])
(;W[kg];B[qg]C[Taking the stone would give Black this chance, so White cannot do this.]))
(;B[qh];W[qg]
(;B[rj];W[rk]C[This should do.])
(;B[qj];W[qi];B[ri];W[pi];B[rh];W[qk];B[rj];W[rk]C[Clever but ill-fated.]))
(;B[kg];W[qk]C[White saves the side. Black will need another move just to capture 3 stones.])
(;B[ma];W[qk])
(;B[qi];W[qh];B[qj];W[pi]C[White lives.])
(;B[ri];W[qh];B[rh];W[sf];B[sb];W[kg]C[White will either fight this ko or create a living shape (at Q11, f.i.)]))