(;AB[aq]AB[bq]AB[cq]AB[dr]AB[er]AW[fr]AW[fq]AW[eq]AW[dq]AW[dp]AW[cp]AW[bp]AW[ap]C[White to kill. Ko is not enough. Play P if you think black can't save this group even if white plays elsewhere (tenuki).]LB[ho:P]AP[goproblems]
(;W[ar];B[br]
(;W[cr];B[cs]C[Black lives.])
(;W[as];B[cs]C[Black lives.])
(;W[bs];B[cr]
(;W[as];B[cs]C[Black lives.])
(;W[cs];B[as]C[Ko.])
(;W[ds];B[as]C[Ko.])
(;W[es];B[as]C[Ko.])
(;W[fs];B[cs]C[Black lives.]))
(;W[cs];B[bs]C[Black lives.])
(;W[ds];B[cs]C[Black lives.])
(;W[es];B[cs]C[Black lives.])
(;W[fs];B[cs]C[Black lives.]))
(;W[br]C[];B[cr]
(;W[ar];B[es]C[Black lives.])
(;W[as];B[ar]
(;W[bs];B[cs]C[Black lives.])
(;W[cs];B[bs]C[Black lives.])
(;W[ds];B[bs]C[Black lives.])
(;W[es];B[bs]C[Black lives.])
(;W[fs];B[bs]C[Black lives.]))
(;W[bs]C[]
(;B[ar]C[CHOICE]
(;W[as];B[cs]C[Black lives.])
(;W[cs]C[Black is dead!RIGHT])
(;W[ds];B[es]C[Black lives.])
(;W[es]C[Black is dead!RIGHT])
(;W[fs];B[es]
(;W[as];B[cs]C[Black lives.])
(;W[cs]C[Black is dead!RIGHT])
(;W[ds];B[cs]C[Black lives.])))
(;B[cs]C[CHOICE]
(;W[ar];B[es]C[Black lives.])
(;W[as];B[es]C[Black lives.])
(;W[ds];B[es]C[Black lives.])
(;W[es]C[Black is dead!RIGHT])
(;W[fs];B[es]C[Black lives.]))
(;B[es]C[CHOICE]
(;W[ar];B[cs]C[Black lives.])
(;W[as];B[cs]C[Black lives.])
(;W[cs]C[Black is dead!RIGHT])
(;W[ds];B[cs]C[Black lives.])
(;W[fs];B[cs]C[Black lives.])))
(;W[cs]C[]
(;B[ar]C[CHOICE]
(;W[as];B[bs]C[Black lives.])
(;W[bs]C[Black is dead!RIGHT])
(;W[ds];B[bs]C[Black lives.])
(;W[es];B[bs]C[Black lives.])
(;W[fs];B[bs]C[Black lives.]))
(;B[as]C[CHOICE]
(;W[ar];B[bs]C[Black lives.])
(;W[bs]C[Black is dead!RIGHT])
(;W[ds];B[es]C[Black lives.])
(;W[es]C[];B[bs]
(;W[ar]C[Black is dead!RIGHT])
(;W[ds];B[fs]C[Black lives.])
(;W[fs];B[ds]C[Black lives.]))
(;W[fs];B[bs]
(;W[ar];B[bs]
(;W[as];B[bs]C[Black lives.])
(;W[ds];B[es]C[Black lives.])
(;W[es]C[Black is dead!RIGHT]))
(;W[ds];B[es]C[Black lives.])
(;W[es];B[ds]C[Black lives.])))
(;B[bs]C[CHOICE]
(;W[ar];B[ds]C[Black lives.])
(;W[as];B[ar]
(;W[bs]C[Black is dead!RIGHT])
(;W[ds];B[bs]C[Black lives.])
(;W[es];B[bs]C[Black lives.])
(;W[fs];B[bs]C[Black lives.]))
(;W[ds];B[es]C[Black lives.])
(;W[es];B[ds]C[Black lives.])
(;W[fs];B[ar]C[Black lives.]))
(;B[es]C[CHOICE]
(;W[ar];B[bs]
(;W[as];B[bs]C[Black lives.])
(;W[fs];B[as]C[Black lives.]))
(;W[as]C[Black is dead!RIGHT])
(;W[bs]C[Black is dead!RIGHT])
(;W[ds];B[bs]C[Black lives.])
(;W[fs];B[bs]C[]
(;W[ar];B[as]C[Black lives.])
(;W[as]C[Black is dead!RIGHT]))))
(;W[ds];B[bs]C[Black lives.])
(;W[es];B[bs]C[]
(;W[ar]C[Black is dead!RIGHT])
(;W[as];B[ar]C[Black lives.])
(;W[cs];B[ds]C[Black lives.])
(;W[ds];B[ar]C[Black lives.])
(;W[fs];B[ds]C[Black lives.]))
(;W[fs];B[bs]C[Black lives.]))
(;W[cr];B[br]
(;W[ar];B[cs]C[Black lives.])
(;W[as];B[cs]C[Black lives.])
(;W[bs];B[cs]C[Black lives.])
(;W[cs];B[bs]C[Black lives.])
(;W[ds];B[cs]C[Black lives.])
(;W[es];B[cs]C[Black lives.])
(;W[fs];B[cs]C[Black lives.]))
(;W[as];B[bs]
(;W[ar];B[cr]C[Black lives.])
(;W[br];B[ar]C[Black lives.])
(;W[cr];B[cs]C[Black lives.])
(;W[cs];B[br]C[Black lives.])
(;W[ds];B[cr]C[Black lives.])
(;W[es];B[cr]C[Black lives.])
(;W[fs];B[cr]C[Black lives.]))
(;W[bs];B[br]
(;W[ar];B[as]MA[ar]
(;W[cr];B[cs]C[Black lives.])
(;W[cs];B[cr]C[Ko.])
(;W[ds];B[cs]C[Black lives.])
(;W[es];B[cs]C[Black lives.])
(;W[fs];B[cs]C[Black lives.]))
(;W[cr];B[cs]C[Black lives.])
(;W[as];B[cs]C[Black lives.])
(;W[cs];B[as]C[Ko.])
(;W[ds];B[cs]C[Ko.])
(;W[es];B[cs]C[Black lives.])
(;W[fs];B[cs]C[Black lives.]))
(;W[cs];B[bs]
(;W[ar];B[br]C[Black lives.])
(;W[br];B[ar]C[Ko.])
(;W[cr];B[br]C[Black lives.])
(;W[as];B[br]C[Black lives.])
(;W[ds];B[cr]C[Black lives.])
(;W[es];B[cr]C[Black lives.])
(;W[fs];B[cr]C[Black lives.]))
(;W[ds];B[cs]
(;W[ar];B[es]C[Black lives.])
(;W[br];B[ar]
(;W[cr];B[bs]C[Black lives.])
(;W[as];B[bs]C[Black lives.])
(;W[bs];B[es]C[Black lives.])
(;W[es];B[fs]C[Black lives.])
(;W[fs];B[es]C[Black lives.]))
(;W[cr];B[br]C[Black lives.])
(;W[as];B[es]C[Black lives.])
(;W[bs];B[es]C[Black lives.])
(;W[es];B[fs]C[]
(;W[ar];B[br]C[Black lives.])
(;W[br];B[ar]C[Black lives.])
(;W[cr];B[br]C[Black lives.])
(;W[as];B[es]C[Black lives.])
(;W[bs];B[es]C[Black lives.])
(;W[ds];B[es]C[Black lives.])
(;W[es];B[br]C[Black lives.])
(;W[gs];B[es]C[Black lives.]))
(;W[fs];B[es]C[Black lives.]))
(;W[es]
(;B[cr]C[CHOICE]
(;W[ar]C[Black is dead!RIGHT])
(;W[br];B[bs]C[]
(;W[ar]C[Black is dead!RIGHT])
(;W[as];B[ar]C[Black lives.])
(;W[cs];B[ds]C[Black lives.])
(;W[ds];B[ar]C[Black lives.])
(;W[fs];B[ds]C[Black lives.]))
(;W[as];B[bs]C[Black lives.])
(;W[bs]C[Black is dead!RIGHT])
(;W[cs];B[bs]C[Black lives.])
(;W[ds]C[Black is dead!RIGHT])
(;W[fs];B[bs]C[Black lives.]))
(;B[cs]C[CHOICE]
(;W[ar];B[br]C[Black lives.])
(;W[br]C[Black is dead!RIGHT])
(;W[cr];B[br]C[Black lives.])
(;W[as];B[br]C[Black lives.])
(;W[bs];B[br]C[Black lives.])
(;W[ds];B[fs]C[]
(;W[ar];B[br]C[Black lives.])
(;W[br]C[];B[ar]C[Black lives.])
(;W[cr];B[br]C[Black lives.])
(;W[as];B[br]C[Black lives.])
(;W[bs];B[br]C[Black lives.])
(;W[ds];B[br]C[Black lives.])
(;W[es];B[br]C[Black lives.])
(;W[gs];B[es]C[Black lives.]))
(;W[fs];B[br]
(;W[ar];B[as]C[Black lives.])
(;W[as];B[ds]C[Black lives.])
(;W[bs];B[as]C[Black lives.])
(;W[ds];B[as]C[Black lives.]))))
(;W[fs];B[br]C[CHOICE]
(;W[ar];B[cs]C[Black lives.])
(;W[cr];B[cs]C[Black lives.])
(;W[as];B[cs]C[Black lives.])
(;W[bs];B[cs]C[Black lives.])
(;W[cs];B[cr]
(;W[ar];B[as]C[Black lives.])
(;W[as];B[bs]C[Black lives.])
(;W[bs];B[as]C[Ko.])
(;W[ds];B[es]C[Black lives.])
(;W[es];B[ds]C[Black lives.]))
(;W[ds];B[cs]
(;W[ar];B[as]C[Black lives.])
(;W[as];B[es]C[Black lives.])
(;W[bs];B[es]C[Black lives.])
(;W[es];B[as]C[Black lives.]))
(;W[es];B[cs]C[Black lives.]
(;W[ar];B[as]C[Black lives.])
(;W[as];B[ds]C[Black lives.])
(;W[bs];B[as]C[Black lives.])
(;W[ds];B[as]C[Black lives.])))
(;W[ho];B[bs]
(;W[ar];B[cr]C[Black lives.])
(;W[br];B[cr]C[Black lives.])
(;W[cr];B[br]C[Black lives.])
(;W[as];B[br]C[Black lives.])
(;W[cs];B[cr]C[Black lives.])
(;W[ds];B[cr]C[Black lives.])
(;W[es];B[cr]C[Black lives.])
(;W[fs];B[cr]C[Black lives.])))