(;AB[ai]AB[bi]AB[ci]AB[bj]AW[ah]AW[bh]AW[ch]AW[di]AW[dg]AW[dj]AB[bl]AB[cn]AB[bo]AB[co]AB[cp]AB[bq]AB[br]AB[cr]AW[bp]AW[cq]AW[dq]AW[dr]AW[dp]AW[do]AW[dn]AW[dk]AW[dl]AW[dm]AW[fr]C[White to reduce.]AP[goproblems]
(;W[bm];B[cm]
(;W[bk]
(;B[ck]C[]
(;W[cl]
(;B[ak]
(;W[cj]
(;B[bk]C[]
(;W[an]
(;B[ao];W[al];B[am]C[This ko is favorable for black. Otherwise, she would have reduced her losses to the marked stones.]TR[ai]TR[bi]TR[ci]TR[bj])
(;B[ap]
(;W[al];B[am]C[This ko is favorable for black. Otherwise, she would have limited her losses to the marked stones.]TR[ai]TR[bi]TR[ci]TR[bj])
(;W[ao];B[al]
(;W[ar];B[bs]C[Ko threats, but no seki.])
(;W[bs];B[ar]C[Ko threats, but no seki.])
(;W[cs];B[bs];W[ar];B[ds]C[Ko threats, but no seki.]))))
(;W[al];B[am])
(;W[ao];B[ap];W[an];B[al]
(;W[ar];B[bs]C[Ko threats, but no seki.])
(;W[bs];B[ar]C[Ko threats, but no seki.])
(;W[cs];B[bs];W[ar];B[ds]C[Ko threats, but no seki.])))
(;B[am];W[bk]C[Ko to take the marked stones. However, they could have been taken cleanly.]TR[ai]TR[bi]TR[ci]TR[bj]))
(;W[an];B[ao]
(;W[cj];B[bk];W[al];B[am]C[This ko is favorable for black. Otherwise, she would have reduced her losses to the marked stones.]TR[ai]TR[bi]TR[ci]TR[bj])
(;W[al];B[am]C[Ko. This ko is favorable for black. Otherwise, she would have sacrificed the marked stones earlier.]TR[ai]TR[bi]TR[ci]TR[bj]))
(;W[am];B[an];W[cj];B[al]))
(;B[al];W[am];B[ak];W[cj];B[an]C[Ko to take the marked stones. However, they could have been killed cleanly.]TR[ai]TR[bi]TR[ci]TR[bj]))
(;W[ak]
(;B[cl];W[cj]C[];B[am]C[Great!RIGHT])
(;B[al]
(;W[cl];B[aj]
(;W[cj];B[am];W[bk]C[Great!RIGHT])
(;W[bk];B[ak]
(;W[am];B[an];W[cj];B[bn])
(;W[cj];B[am])))
(;W[cj];B[cl];W[aj]C[The stones are taken, but black's position is more secure than it needs to be.RIGHT]))))
(;B[cl];W[ck];B[ak];W[cj]C[Great! Black is avoiding the risk of a ko for a larger set of stones.RIGHT]))
(;W[cl];B[bk]
(;W[bn];B[ap])
(;W[al];B[an]
(;W[am];B[ak])
(;W[ap];B[aq])))
(;W[al];B[bk];W[cl];B[an]
(;W[am];B[ak])
(;W[ap];B[aq])))
(;W[cl];B[bk];W[bm];B[cm]
(;W[bn];B[ap])
(;W[al];B[an]
(;W[am];B[ak])
(;W[ap];B[aq])))
(;W[cm];B[bm];W[bk];B[ck];W[cj];B[ak])
(;W[bk];B[ck]C[]
(;W[bm];B[cm]
(;W[cl]
(;B[ak]
(;W[cj]
(;B[bk]C[]
(;W[an]
(;B[ao];W[al];B[am]C[This ko is favorable for black. Otherwise, she would have reduced her losses to the marked stones.]TR[ai]TR[bi]TR[ci]TR[bj])
(;B[ap]
(;W[al];B[am]C[This ko is favorable for black. Otherwise, she would have limited her losses to the marked stones.]TR[ai]TR[bi]TR[ci]TR[bj])
(;W[ao])))
(;W[al];B[am])
(;W[ao];B[ap];W[an];B[al]
(;W[ar];B[bs]C[Ko threats, but no seki.])
(;W[bs];B[ar]C[Ko threats, but no seki.])
(;W[cs];B[bs];W[ar];B[ds]C[Ko threats, but no seki.])))
(;B[am];W[bk]C[Ko to take the marked stones. However, they could have been taken cleanly.]TR[ai]TR[bi]TR[ci]TR[bj]))
(;W[an];B[ao]
(;W[cj];B[bk])
(;W[al];B[am]C[Ko. This ko is favorable for black. Otherwise, she would have sacrificed the marked stones earlier.]TR[ai]TR[bi]TR[ci]TR[bj]))
(;W[am];B[an];W[cj];B[al]))
(;B[al];W[am];B[ak];W[cj];B[an]C[Ko to take the marked stones. However, they could have been killed cleanly.]TR[ai]TR[bi]TR[ci]TR[bj]))
(;W[ak]
(;B[cl];W[cj]C[];B[am]C[Great!RIGHT])
(;B[al]
(;W[cl];B[aj]
(;W[cj];B[am];W[bk]C[Great!RIGHT])
(;W[bk];B[ak]
(;W[am];B[an];W[cj];B[bn])
(;W[cj];B[am])))
(;W[cj];B[cl];W[aj]C[The stones are taken, but black's position is more secure than it needs to be.RIGHT]))))
(;W[cl];B[ak];W[bm];B[cm]
(;W[cj]
(;B[bk]C[]
(;W[an]
(;B[ao];W[al];B[am]C[This ko is favorable for black. Otherwise, she would have reduced her losses to the marked stones.]TR[ai]TR[bi]TR[ci]TR[bj])
(;B[ap]
(;W[al];B[am]C[This ko is favorable for black. Otherwise, she would have limited her losses to the marked stones.]TR[ai]TR[bi]TR[ci]TR[bj])
(;W[ao])))
(;W[al];B[am])
(;W[ao];B[ap];W[an];B[al]
(;W[ar];B[bs]C[Ko threats, but no seki.])
(;W[bs];B[ar]C[Ko threats, but no seki.])
(;W[cs];B[bs];W[ar];B[ds]C[Ko threats, but no seki.])))
(;B[am];W[bk]C[Ko to take the marked stones. However, they could have been taken cleanly.]TR[ai]TR[bi]TR[ci]TR[bj]))
(;W[an];B[ao]
(;W[cj];B[bk])
(;W[al];B[am]C[Ko. This ko is favorable for black. Otherwise, she would have sacrificed the marked stones earlier.]TR[ai]TR[bi]TR[ci]TR[bj]))
(;W[am];B[an];W[cj];B[al]))
(;W[ak];B[cl];W[cj]C[Great!RIGHT])))