(;AW[qa]AW[rb]AW[qc]AW[pb]AW[ob]AW[nc]AW[nd]AW[oe]AW[pe]AW[qd]AB[rd]AB[qe]AB[rf]AB[pf]AB[of]AB[ne]AB[nf]AB[md]AB[mc]AB[nb]AB[na]AB[mb]AB[pa]AB[oa]C[Black to kill]AP[goproblems]
(;B[od];W[rc]
(;B[pc];W[sc]
(;B[sa]C[White is dead because white cannot catch the two black stones and therefore has only one eyeRIGHT])
(;B[ra];W[sa])
(;B[oc];W[sa];B[qb];W[pb];B[ob];W[qb])
(;B[sb];W[sa])
(;B[pd];W[sa]))
(;B[pd];W[pc])
(;B[oc];W[pc]
(;B[sc];W[sb];B[ra];W[sa])
(;B[sb];W[sc];B[ra];W[sa])
(;B[ra];W[sa]))
(;B[ra];W[sa]
(;B[pc];W[sc])
(;B[sc];W[pc]
(;B[sd];W[sb])
(;B[sb];W[sd]))
(;B[sb];W[sc]))
(;B[sc]
(;W[sb]C[CHOICE]
(;B[pc]C[White is dead because white cannot catch the two black stones and therefore has only one eyeRIGHT])
(;B[ra];W[pc]
(;B[pd];W[sa])
(;B[oc];W[sa])
(;B[qb]C[Only a Ko]))
(;B[oc];W[pc];B[ra];W[sa])
(;B[pd];W[pc];B[ra];W[sa])
(;B[sd];W[pc];B[ra];W[sa]))
(;W[pc]C[This white move is only for navigation purposes (in answer to a comment of someone who thought this would end in ko). All 'solved' variations beyond this point are just the result of white playing weakly.]
(;B[sb];W[sa]
(;B[sd]C[No koRIGHT])
(;B[ra]C[If black plays s19, white must not try to play ko but know that it's dead as it stands. If he does, however, he will only waste a ko-threat. To show this, play at A as an imaginary ko-threat.FORCE]LB[lf:A];W[lf]LB[le:A]C[Play black at A as an answer to white's ko threatFORCE];B[le];W[sa]C[White now recaptured the ko, spent a ko threat but black will just connect at AFORCE]LB[sd:A];B[sd]C[And all white's hopes of living are gone, along with one of white's precious ko threats.RIGHT]))
(;B[ra];W[sa]
(;B[sd];W[sb])
(;B[sb];W[sd]))
(;B[sa];W[sb])))
(;B[sb];W[sc]
(;B[pc];W[sa])
(;B[ra];W[sa])
(;B[sa];W[pc]))
(;B[sd];W[pc]
(;B[sc];W[sb];B[ra];W[sa])
(;B[ra];W[sa]
(;B[sc];W[sb])
(;B[sb];W[sc]))
(;B[sb];W[sc];B[ra];W[sa]))
(;B[sa];W[pc]
(;B[ra];W[sb];B[ra];W[sa])
(;B[sc];W[sb])))
(;B[pd];W[pc]
(;B[od];W[rc])
(;B[oc];W[od])
(;B[rc];W[od])
(;B[sc];W[od])
(;B[ra];W[sa]
(;B[rc];W[od])
(;B[sc];W[od]))
(;B[sb];W[od]))
(;B[rc];W[od]
(;B[pc];W[sb]
(;B[oc];W[pd];B[ra];W[sa])
(;B[pd];W[oc];B[ra];W[sa])
(;B[ra];W[sa]
(;B[oc];W[pd])
(;B[pd];W[oc])))
(;B[sb];W[pc])
(;B[ra];W[qb]
(;B[sb];W[pc])
(;B[pc];W[sb]
(;B[oc];W[pd])
(;B[pd];W[oc]))
(;B[pd];W[pc])
(;B[oc];W[pc]))
(;B[pd];W[pc])
(;B[oc];W[pc]))
(;B[sc];W[od]
(;B[pc];W[sb]
(;B[ra];W[sa]
(;B[pd];W[oc])
(;B[oc];W[pd]))
(;B[oc];W[pd];B[ra];W[sa])
(;B[pd];W[oc];B[ra];W[sa]))
(;B[oc];W[pc])
(;B[pd];W[pc])
(;B[ra];W[sa]
(;B[sb];W[pc])
(;B[pc];W[sb]
(;B[pd];W[oc])
(;B[oc];W[pd]))
(;B[oc];W[pc])
(;B[pd];W[pc]))
(;B[sb];W[pc]))
(;B[oc];W[pc]
(;B[od];W[rc]
(;B[sc];W[sb];B[ra];W[sa])
(;B[sb];W[sc];B[ra];W[sa])
(;B[ra];W[sa]))
(;B[pd];W[od])
(;B[rc];W[od])
(;B[ra];W[sa]
(;B[rc];W[od])
(;B[sc];W[od])
(;B[od];W[rc])))
(;B[pc];W[pd]
(;B[oc];W[od]
(;B[rc];W[sb];B[ra];W[sa])
(;B[ra];W[sa]
(;B[sc];W[rc])
(;B[sb];W[sc]))
(;B[sb];W[sc]
(;B[ra];W[sa])
(;B[rc];W[sa];B[sd];W[sb])
(;B[sa];W[rc])))
(;B[od];W[oc])
(;B[rc];W[oc])
(;B[sb];W[sc]
(;B[rc];W[sa]
(;B[oc];W[od];B[sd];W[sb])
(;B[sd];W[sb]
(;B[oc];W[od])
(;B[od];W[oc]))
(;B[od];W[oc]))
(;B[ra];W[sa])
(;B[sd];W[rc]
(;B[oc];W[od];B[ra];W[sa])
(;B[ra];W[sa]))
(;B[oc];W[od]
(;B[ra];W[sa])
(;B[rc];W[sa];B[sd];W[sb]))
(;B[od];W[oc]))
(;B[ra];W[sa]
(;B[sc];W[sb]
(;B[oc];W[od])
(;B[od];W[oc]))
(;B[sb];W[sc]))
(;B[sc];W[sb]
(;B[ra];W[sa]
(;B[oc];W[od])
(;B[od];W[oc]))
(;B[oc];W[od];B[ra];W[sa])
(;B[od];W[oc])))
(;B[ra];W[od]
(;B[pc];W[sa]
(;B[sc];W[sb]
(;B[pd];W[oc])
(;B[oc];W[pd]))
(;B[oc];W[pd]
(;B[sc];W[rc])
(;B[sb];W[sc]))
(;B[pd];W[oc])
(;B[sb];W[sc]
(;B[pd];W[oc])
(;B[oc];W[pd])))
(;B[pd];W[pc])
(;B[oc];W[pc]))
(;B[sb];W[od]
(;B[pc];W[sc]
(;B[rc];W[sa]
(;B[sd];W[sb]
(;B[pd];W[oc])
(;B[oc];W[pd]))
(;B[oc];W[pd];B[sd];W[sb])
(;B[pd];W[oc]))
(;B[pd];W[oc])
(;B[oc];W[pd]
(;B[rc];W[sa];B[sd];W[sb])
(;B[sd];W[rc];B[ra];W[sa])
(;B[ra];W[sa])
(;B[sa];W[rc]))
(;B[ra];W[sa]
(;B[pd];W[oc])
(;B[oc];W[pd]))
(;B[sd];W[rc]
(;B[pd];W[oc])
(;B[oc];W[pd];B[ra];W[sa])
(;B[ra];W[sa]
(;B[pd];W[oc])
(;B[oc];W[pd])))
(;B[sa];W[rc]
(;B[pd];W[oc])
(;B[oc];W[pd])))
(;B[oc];W[pc])
(;B[pd];W[pc])
(;B[rc];W[pc])
(;B[sc];W[pc])
(;B[ra];W[sa];B[sc];W[pc])
(;B[sd];W[pc]))
(;B[sa];W[od]
(;B[pc];W[rc]
(;B[ra];W[sb]
(;B[ra];W[sa]
(;B[pd];W[oc])
(;B[oc];W[pd]))
(;B[oc];W[pd];B[ra];W[sa])
(;B[pd];W[oc];B[ra];W[sa]))
(;B[pd];W[oc]
(;B[ra];W[sb];B[ra];W[sa])
(;B[sc];W[sb])
(;B[sb];W[sc]))
(;B[oc];W[pd];B[ra];W[sb];B[ra];W[sa]))
(;B[pd];W[pc])
(;B[oc];W[pc]))
(;B[sd];W[od]
(;B[pc];W[rc]
(;B[oc];W[pd])
(;B[pd];W[oc]
(;B[ra];W[sa])
(;B[sb];W[sc]))
(;B[ra];W[sa];B[oc];W[pd]))
(;B[pd];W[pc])
(;B[oc];W[pc])
(;B[ra];W[sa]
(;B[pd];W[pc])
(;B[oc];W[pc]))
(;B[sb];W[pc])))