(;AW[qc]AW[qb]AW[pc]AW[ob]AW[oa]AB[oc]AB[nc]AB[nb]AB[na]AB[pd]AB[qd]AB[qg]AB[rh]AB[qa]TR[qa]C[Black just played the marked stone. White to live.]AP[goproblems]
(;W[ra]
(;B[rb]
(;W[rc];B[sa]
(;W[sc];B[pb]
(;W[sb]
(;B[pa];W[ra]C[Correct! Black couldn't connect due to a shortage of liberties.RIGHT])
(;B[ra];W[pa]C[For the sake of reference.RIGHT]))
(;W[pa];B[pb]C[Close, but not quite.]))
(;W[pb];B[rd];W[sc];B[sd]C[White can't approach.])
(;W[sb];B[sc];W[sd];B[pb];W[sb]C[White makes an unnecessary ko.])
(;W[sd];B[pb];W[sb]C[White makes an unnecessary ko.]))
(;W[pa];B[rc])
(;W[sb];B[rc]
(;W[pa];B[rd])
(;W[rd];B[pb])))
(;B[rc]
(;W[rb]
(;B[rd]
(;W[pa]C[RIGHT])
(;W[sb]C[RIGHT]))
(;B[pa]
(;W[rd]C[RIGHT])
(;W[pb];B[rd];W[sb]C[RIGHT])))
(;W[sb];B[rb]
(;W[pa];B[rd])
(;W[rd];B[pb]))
(;W[rd];B[rb];W[pa];B[re])))
(;W[rd];B[rb]
(;W[rc];B[pb]
(;W[ra];B[sa];W[sc];B[pa])
(;W[sb];B[ra])
(;W[sc];B[ra])
(;W[sd];B[ra]))
(;W[ra];B[sa];W[rc];B[pb];W[sc];B[pa])
(;W[pb];B[rc])
(;W[sb];B[rc]))
(;W[rc];B[ra]
(;W[rd];B[re]
(;W[sd];B[pb])
(;W[pb];B[sd];W[sc]C[White can't even force a seki here.])
(;W[sb];B[sd]
(;W[rb];B[pb])
(;W[pb]C[Black can tenuki.])))
(;W[sb];B[rd])
(;W[sc];B[pb];W[re];B[rd];W[sd];B[qf]))
(;W[sc];B[rb]
(;W[rc];B[ra];W[pb]C[];B[rd]C[Dead shape on the inside.])
(;W[rd];B[rc]))
(;W[sb];B[ra]
(;W[rd];B[re];W[pb]
(;B[rc];W[sd];B[se]
(;W[rb];B[sc])
(;W[sc];B[rb]))
(;B[sd];W[rc]))
(;W[rb];B[pb];W[rd];B[re])
(;W[rc];B[pb]))
(;W[pb];B[rc];W[rb];B[rd]))
