(;AB[rc]AB[qc]AB[pb]AB[ob]AB[qa]AB[pd]AB[od]AB[nd]AB[pe]AB[of]AW[qd]AW[rd]AW[sd]AB[qf]AB[sf]AW[pc]AW[oc]AW[nc]AW[nb]AW[mc]AW[lb]AW[na]AW[ld]AB[md]AB[me]AB[nf]C[]AP[goproblems]
(;W[sc];B[rb]C[]
(;W[oa];B[sb];W[pa];B[re]C[3 liberties against 2.])
(;W[sb];B[ra]
(;W[oa];B[re]
(;W[pa];B[qe];W[qb];B[pb])
(;W[sa];B[qe]))
(;W[sa];B[oa])))
(;W[sb];B[rb]
(;W[sc];B[ra]C[]
(;W[oa];B[re]
(;W[pa];B[qe];W[qb];B[pb])
(;W[sa];B[qe]))
(;W[sa];B[oa]))
(;W[ra];B[oa];W[sc];B[sa]C[Only ko.]))
(;W[rb]C[This is the critical point. Well done!(Well, prove it! : edit by BartTM)];B[sb]
(;W[oa];B[ra])
(;W[ra];B[sc];W[oa];B[re];W[pa];B[qe];W[qb];B[se])
(;W[sc];B[qb]
(;W[sa];B[oa];W[sb];B[re];W[ra]C[RIGHT])
(;W[oa];B[ra])
(;W[ra];B[sa]
(;W[oa];B[re]
(;W[rb];B[se];W[ra]C[RIGHT])
(;W[ra];B[se];W[rb]C[RIGHT])
(;W[pa];B[qe]))
(;W[rb];B[re]
(;W[ra];B[sb]
(;W[sa];B[sb])
(;W[oa];B[sa]
(;W[rb];B[se];W[ra]C[RIGHT])
(;W[ra];B[se];W[rb]C[RIGHT])
(;W[pa];B[qe])))
(;W[oa];B[se];W[ra]C[RIGHT])
(;W[pa]
(;B[oa])
(;B[qe]
(;W[ra]C[RIGHT])
(;W[oa];B[se]))))
(;W[ra];B[re]
(;W[oa];B[se];W[rb]C[RIGHT])
(;W[pa];B[qe]
(;W[rb]C[RIGHT])
(;W[oa];B[se])))
(;W[pa];B[oa]))
(;W[pa];B[ra])))
(;W[oa];B[rb]
(;W[pa];B[sc]
(;W[qb];B[pb]
(;W[sa];B[re]C[White loses the capturing race.])
(;W[ob];B[re]C[Black still has 3 liberties and White has 2.]))
(;W[sa];B[re]))
(;W[sc];B[sb];W[pa];B[re]C[3 liberties against 2.])
(;W[sb];B[sc]
(;W[sa];B[pa])
(;W[pa];B[sa]))))