(;AB[ob]AB[nb]AB[nd]AB[od]AB[oe]AB[pf]AB[pg]AB[rg]AB[rf]AB[re]AW[pb]AW[pc]AW[pd]AW[pe]AB[pa]AB[qd]AW[qe]AW[rd]TR[pa]C[Grebble found this nice attack against the corner.]AP[goproblems]
(;W[rb];B[ra]
(;W[qc];B[sc]
(;W[qa];B[qb]
(;W[sb];B[sd]
(;W[qa]MA[oa]C[Black has to find the first ko threat elsewhere, and White has an extra ko threat at P19 to boot.RIGHT])
(;W[se];B[qa])
(;W[sa];B[rc])
(;W[oa];B[na]C[];W[qa]C[Ko, Black has to find the first threat. This is nearly as good as the solution, in which White has an extra internal ko threat.])
(;W[rc];B[qa]))
(;W[qa]C[NOTTHIS])
(;W[sd];B[sb]
(;W[qa]MA[sd]MA[sb]C[Black has to find a ko threat somewhere else. The T16-T18 exchange gets a few points more than T18-T16, but now White doesn't have the extra ko threat at P19.]MA[oa])
(;W[rc];B[qa])
(;W[oa];B[rc];W[qa];B[se]
(;W[rb];B[qd])
(;W[qd];B[rb]
(;W[sa];B[rb]MA[rc]MA[sb])
(;W[pa]C[White is dead. If White captures, Black throws in at S18.]MA[rb]))))
(;W[sa];B[sb]
(;W[qa]C[Ko, Black has to find the first threat. In the solution White has an internal ko threat; here there isn't one so this is not as good.])
(;W[rc];B[qa])
(;W[sd];B[rc]))
(;W[rc];B[qa]
(;W[sd];B[sb])
(;W[sb];B[sd]))
(;W[oa];B[na]C[This just wastes a ko threat.]))
(;W[sd];B[sb]
(;W[qa];B[qb]C[Since a ko where Black takes first is not as good as the solution, White wants to find something better than a ko threat elsewhere.]
(;W[oa];B[rc];W[qa];B[se]
(;W[rb];B[qd])
(;W[qd];B[rb]
(;W[sa];B[rb]MA[rc]MA[sb])
(;W[pa]C[White is dead. If White captures, Black throws in at S18.]MA[rb])))
(;W[qa]C[NOTTHIS])
(;W[rc];B[qa]))
(;W[qb];B[qa])
(;W[rc];B[qa]
(;W[sa];B[sb])
(;W[oa];B[na];W[sa];B[sb]))
(;W[oa];B[qa]
(;W[rc];B[na];W[sa];B[sb])
(;W[qb];B[na])))
(;W[qb];B[qa])
(;W[sb];B[sd]
(;W[qa];B[qb]
(;W[sa];B[rc])
(;W[rc];B[qa])
(;W[se];B[qa])
(;W[oa];B[na]C[];W[qa]C[Ko, Black has to find the first threat. This is nearly as good as the solution, in which White has an extra internal ko threat.]))
(;W[qb];B[qa])
(;W[rc];B[qa];W[se];B[sd])
(;W[sa];B[qa])
(;W[oa];B[qa])
(;W[se];B[qa]))
(;W[rc];B[qa]
(;W[sd];B[sb]
(;W[sa];B[sb])
(;W[oa];B[na];W[sa];B[sb]))
(;W[sb];B[sd];W[se];B[sd]))
(;W[sa];B[qa]
(;W[sb];B[sd])
(;W[sd];B[sb])
(;W[qb];B[sb])
(;W[oa];B[sb]))
(;W[oa];B[qa]
(;W[sa];B[sb])
(;W[qb];B[na])
(;W[sb];B[sd])
(;W[sd];B[sb]
(;W[rc])
(;W[qb];B[na]))))
(;W[qb];B[qa]
(;W[qc];B[sc])
(;W[sd];B[sb]
(;W[qc];B[sc])
(;W[sc];B[qc]))
(;W[sc];B[qc])
(;W[sb];B[sd])
(;W[oa];B[na]
(;W[sc];B[qc])
(;W[qc];B[sc])
(;W[sd];B[sb]
(;W[qc];B[sc])
(;W[sc];B[qc]))
(;W[sb];B[sd]))
(;W[sa];B[oa]
(;W[sd];B[sb]
(;W[sc];B[qc])
(;W[qc];B[sc]))
(;W[qc];B[sc]
(;W[sd];B[sb])
(;W[sb];B[sd]))
(;W[sc];B[qc])
(;W[sb];B[sd])))
(;W[qa];B[qb]
(;W[qc];B[sb]
(;W[sc];B[rc]C[Ko, White has to find the first ko threat.])
(;W[qa]C[Ko, Black has to find the first ko threat. This is almost as good as the solution in which White also has an internal ko threat.])
(;W[rc];B[qa])
(;W[sd];B[qa])
(;W[oa];B[rc]
(;W[qa];B[sd]
(;W[rb];B[sc])
(;W[se];B[sc])
(;W[qd];B[rb])
(;W[pa];B[rb]))
(;W[sd];B[na])
(;W[sc];B[sd])))
(;W[rc];B[qa])
(;W[sc];B[qc])
(;W[sb];B[qc])
(;W[sd];B[qc])
(;W[sa];B[sb]
(;W[qc];B[rc])
(;W[rc];B[qa])
(;W[sc];B[rc])))
(;W[rc];B[qa])
(;W[sb];B[qc]
(;W[qb];B[qa]
(;W[sd];B[rc];W[sc];B[qc])
(;W[rc];B[sd])
(;W[sa];B[oa]
(;W[sd];B[rc];W[sc];B[qc])
(;W[rc];B[sd]))
(;W[oa];B[na]
(;W[sd];B[rc];W[sc];B[qc])
(;W[rc];B[sd])
(;W[sa];B[oa]
(;W[sd];B[rc];W[sc];B[qc])
(;W[rc];B[sd]))))
(;W[rc];B[qa]
(;W[qb];B[sd])
(;W[sa];B[sd])
(;W[oa];B[na];W[sa];B[oa];W[qb];B[sd])
(;W[sd];B[qb]))
(;W[qa];B[qb])
(;W[sd];B[qb])
(;W[sa];B[rc]
(;W[sd];B[se])
(;W[sc];B[sd])
(;W[qb];B[sd])))
(;W[sd]
(;B[qa])
(;B[qc]
(;W[qb];B[qa]
(;W[sb];B[rc];W[sc];B[qc])
(;W[rc];B[sb]))
(;W[rc];B[sb]
(;W[qb];B[qa])
(;W[qa];B[qb];W[qa];B[qb])
(;W[sc];B[qa]))
(;W[sb];B[qb])
(;W[qa];B[qb])))
(;W[sc];B[qc]
(;W[qb];B[qa])
(;W[qa];B[qb])
(;W[rc];B[qa]))
(;W[sa];B[qa]
(;W[qc];B[sc]
(;W[sb];B[sd])
(;W[sd];B[sb])
(;W[qb];B[sb])
(;W[oa];B[sb]))
(;W[qb];B[oa]
(;W[sd];B[sb]
(;W[sc];B[qc])
(;W[qc];B[sc]))
(;W[qc];B[sc]
(;W[sd];B[sb])
(;W[sb];B[sd]))
(;W[sc];B[qc])
(;W[sb];B[sd]))
(;W[sd];B[sb])
(;W[sb];B[qc]
(;W[qb];B[oa]
(;W[sd];B[rc];W[sc];B[qc])
(;W[rc];B[sd]))
(;W[rc];B[sd])
(;W[sd];B[qb]))
(;W[sc];B[qc]))
(;W[oa];B[qa]
(;W[qc];B[sc]
(;W[sa])
(;W[qb];B[na])
(;W[sb];B[sd])
(;W[sd];B[sb]))
(;W[qb];B[na]
(;W[sc];B[qc])
(;W[qc];B[sc])
(;W[sd];B[sb]
(;W[qc];B[sc])
(;W[sc];B[qc]))
(;W[sb];B[sd]))
(;W[sd];B[qc]
(;W[qb];B[na]
(;W[rc];B[sb])
(;W[sb];B[rc];W[sc];B[qc]))
(;W[rc];B[na]
(;W[sa];B[sb])
(;W[qb];B[sb])
(;W[sb];B[qb]))
(;W[sb];B[qb])
(;W[sa];B[sb];W[qb];B[na]))
(;W[sa];B[sb]
(;W[qb];B[na]
(;W[sc];B[qc])
(;W[qc];B[sc]))
(;W[qc];B[sc])
(;W[sc];B[qc]
(;W[sa];B[na])
(;W[qb];B[na])))
(;W[sc];B[qc]
(;W[qb];B[na])
(;W[sa];B[na]))))
(;W[qa];B[rc]
(;W[qc];B[rb]
(;W[sd];B[sc]
(;W[ra];B[se]
(;W[qd];B[sb])
(;W[sb];B[qd])
(;W[qb];B[qd]))
(;W[sb];B[se]
(;W[qd];B[sa]C[White is dead. Black can take all outside liberties, then give atari at S19. If White plays S19 or R18 White plays T18 to create a 5 stone nakade shape.])
(;W[ra];B[qd])
(;W[qb];B[qd])
(;W[sa];B[qd])
(;W[oa];B[qd]))
(;W[qb];B[se]
(;W[qd];B[sb])
(;W[ra];B[qd])
(;W[sb];B[qd]))
(;W[qd];B[oa];W[qb];B[sb])
(;W[oa];B[se]
(;W[qd]C[White is dead. Black can take all outside liberties, then give atari at S19. If White plays T19, S19 or R18 White plays T18 to create a 4 stone nakade shape. T19 then T18 etc.])
(;W[sb];B[qd])
(;W[ra];B[qd])
(;W[qb];B[qd])))
(;W[sc];B[sb]
(;W[sd];B[se]
(;W[qd];B[ra]MA[rb]C[If White captures the Black stones Black will play S18 to reduce the corner group to one eye.])
(;W[oa];B[qd])
(;W[ra];B[qd]))
(;W[oa];B[sd]))
(;W[oa];B[sd])
(;W[ra];B[sd])
(;W[qb];B[sd]))
(;W[sd];B[qc])
(;W[rb];B[qc])
(;W[oa];B[qc]))
(;W[qb];B[rc]
(;W[sd];B[sc];W[qc];B[se];W[qd];B[qa]
(;W[ra];B[sb];W[oa];B[pa])
(;W[rb];B[ra])
(;W[sb];B[ra]))
(;W[qc];B[sd];W[rb];B[sc]))
(;W[qc];B[rb]
(;W[qa];B[rc]
(;W[sd];B[sc]
(;W[ra];B[se]
(;W[qd];B[sb])
(;W[sb];B[qd])
(;W[qb];B[qd]))
(;W[sb];B[se]
(;W[qd];B[sa]C[White is dead. Black can take all outside liberties, then give atari at S19. If White plays S19 or R18 White plays T18 to create a 5 stone nakade shape.])
(;W[ra])
(;W[qb];B[qd])
(;W[sa];B[qd])
(;W[oa];B[qd]))
(;W[qb];B[se]
(;W[qd];B[sb])
(;W[ra])
(;W[sb]))
(;W[qd];B[oa];W[qb];B[sb])
(;W[oa];B[se]
(;W[qd]C[White is dead. Black can take all outside liberties, then give atari at S19. If White plays T19, S19 or R18 White plays T18 to create a 4 stone nakade shape. T19 then T18 etc.])
(;W[sb])
(;W[ra];B[qd])
(;W[qb];B[qd])))
(;W[sc];B[sb]
(;W[sd];B[se]
(;W[qd];B[ra]MA[rb]C[If White captures the Black stones Black will play S18 to reduce the corner group to one eye.])
(;W[oa];B[qd])
(;W[ra];B[qd]))
(;W[oa];B[sd]))
(;W[oa];B[sd])
(;W[ra];B[sd])
(;W[qb];B[sd]))
(;W[rc];B[qa])
(;W[qb];B[qa])
(;W[sd];B[qa])
(;W[sc];B[qa])
(;W[oa];B[qa]))
(;W[rc];B[ra]
(;W[qb];B[qa])
(;W[qa];B[qb]
(;W[qc];B[rb])
(;W[rb];B[qa]))
(;W[rb];B[qa]))
(;W[ra];B[rc]
(;W[qc];B[sd]
(;W[rb];B[sc])
(;W[qa];B[rb])
(;W[sb];B[sc]))
(;W[rb];B[qc])
(;W[sd];B[qc]))
(;W[sd];B[rb]
(;W[qa];B[rc];W[qc];B[sc]
(;W[ra];B[se]
(;W[qd];B[sb])
(;W[sb];B[qd])
(;W[qb];B[qd]))
(;W[sb];B[se]
(;W[qd];B[sa]C[White is dead. Black can take all outside liberties, then give atari at S19. If White plays S19 or R18 White plays T18 to create a 5 stone nakade shape.])
(;W[ra])
(;W[qb];B[qd])
(;W[sa];B[qd])
(;W[oa];B[qd]))
(;W[qb];B[se]
(;W[qd];B[sb])
(;W[ra])
(;W[sb]))
(;W[qd];B[oa];W[qb];B[sb])
(;W[oa];B[se]
(;W[qd]C[White is dead. Black can take all outside liberties, then give atari at S19. If White plays T19, S19 or R18 White plays T18 to create a 4 stone nakade shape. T19 then T18 etc.])
(;W[sb])
(;W[ra];B[qd])
(;W[qb];B[qd])))
(;W[qb];B[qa])
(;W[qc];B[qb])
(;W[rc];B[qb])
(;W[oa];B[qa]))
(;W[sc];B[rb]
(;W[qa];B[rc]
(;W[qc];B[sb]
(;W[sd];B[se]
(;W[qd];B[ra]MA[rb]C[If White captures the Black stones Black will play S18 to reduce the corner group to one eye.])
(;W[oa];B[qd])
(;W[ra];B[qd]))
(;W[oa];B[sd]))
(;W[sd];B[qc])
(;W[se];B[qc]
(;W[sb];B[sf])
(;W[ra];B[sb])
(;W[qb];B[sb])))
(;W[rc];B[qa])
(;W[qb];B[qa])
(;W[qc];B[qb])
(;W[ra];B[qb])
(;W[sb];B[qb]))
(;W[sb];B[rb]
(;W[qa];B[rc]
(;W[qc];B[sd])
(;W[sd];B[qc]))
(;W[rc];B[qb])
(;W[qb];B[rc];W[qc]
(;B[sd];W[ra];B[qd])
(;B[ra];W[qa];B[sd]))
(;W[qc];B[qa])
(;W[sd];B[qb])
(;W[ra];B[qb]))
(;W[oa];B[rc]
(;W[qc];B[rb]
(;W[sd];B[sc]
(;W[sb];B[se]
(;W[qd];B[sa])
(;W[ra];B[qd])
(;W[qb];B[qd]))
(;W[ra];B[se]
(;W[qb];B[qd])
(;W[qd];B[sb])
(;W[sb];B[qd])
(;W[qa];B[qd]))
(;W[qb];B[se];W[qd];B[sb])
(;W[qa];B[se]
(;W[qd]C[White is dead. Black can take all outside liberties, then give atari at S19. If White plays T19, S19 or R18 White plays T18 to create a 4 stone nakade shape. T19 then T18 etc.])
(;W[sb])
(;W[ra];B[qd])
(;W[qb];B[qd]))
(;W[qd];B[qa]))
(;W[qa];B[sd])
(;W[qd];B[sd])
(;W[sc];B[sb];W[sd];B[se];W[qd];B[ra]))
(;W[sd];B[qc])))