(;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])))