(;AW[rc]AW[re]AW[qd]AW[pd]AW[pc]AB[qb]AW[pb]AW[pa]AB[ob]AB[oc]AB[oe]AB[pe]AB[qe]AB[od]AB[mb]AB[rf]AB[rg]AB[se]C[Be careful. Only the best result gives you a correct answer.]AP[goproblems]
(;B[sb];W[sd]
(;B[rb];W[sf]C[]
(;B[sg];W[ra]
(;B[se]C[white fights a direct ko for seki, or 3 step ko for lifeRIGHT])
(;B[qa];W[qc];B[se];W[sc]))
(;B[ra];W[sc];B[sg];W[qc]C[slightly worse than the answer (if white wins the ko, black needs another move to make a seki)])
(;B[sc];W[ra]
(;B[sg];W[qa];B[se];W[rd])
(;B[qa];W[qc]
(;B[oa];W[sa])
(;B[sg];W[sa]))))
(;B[sf];W[rb];B[rd];W[sc];B[ra];W[re]C[white lives in double ko])
(;B[rd];W[md]C[Please reply to the ko threat at KFORCE]LB[me:K];B[me];W[re]LB[mf:K]C[Play K (n14) if you want to use a ko threat]
(;B[rb];W[sf]
(;B[sg];W[ra];B[se]C[white fights a direct ko for seki, or 3 step ko for lifeRIGHT])
(;B[ra];W[sc];B[sg];W[qc]C[slightly worse than the answer (if white wins the ko, black needs another move to make a seki)]))
(;B[sf];W[rb];B[rd];W[sc];B[ra];W[re]C[white lives in double ko])))
(;B[rb];W[sb]
(;B[ra];W[rd]
(;B[sd];W[qa])
(;B[sa];W[qa];B[sc];W[qc])
(;B[sc];W[qa];B[sa];W[qc]))
(;B[rd];W[ra];B[sc];W[sd]C[not good enough (see correct solution)]))
(;B[rd];W[rb])
(;B[sc];W[sb]
(;B[rd];W[rb])
(;B[rb];W[sd]C[not good enough (see correct solution)])
(;B[sd];W[rb]))
(;B[ra];W[rb]))