(;AB[qb]AB[pc]AB[oc]AB[rc]AB[qc]AW[ob]AW[pb]AW[qa]AW[rb]AW[nc]AW[mc]AB[oe]C[Black to play in the endgame. Assume white wins any ko and try to avoid unnecessary moves.]AP[goproblems]
(;B[ra];W[sa]
(;B[sc];W[nb]
(;B[sb];W[pa];B[ra]C[Good work!RIGHT])
(;B[pa];W[oa];B[sb]C[RIGHT]))
(;B[pa];W[nb]
(;B[sc];W[oa];B[sb]C[RIGHT])
(;B[ra]C[Ko.]))
(;B[nb];W[mb]
(;B[pa];W[oa];B[sc];W[na];B[sb]C[RIGHT])
(;B[sc];W[na]
(;B[sb];W[pa];B[ra]C[RIGHT])
(;B[pa];W[oa];B[sb]C[RIGHT]))
(;B[na];W[ma];B[sc];W[oa];B[sb]C[RIGHT])))
(;B[sb];W[ra]C[Black can do better.])
(;B[pa];W[oa]
(;B[ra];W[sa]
(;B[nb];W[mb];B[sc];W[na];B[sb]C[RIGHT])
(;B[sc];W[nb];B[sb]C[RIGHT]))
(;B[sb];W[ra])
(;B[nb];W[mb];B[ra];W[sa];B[sc];W[na];B[sb]C[RIGHT]))
(;B[nb];W[pa]
(;B[ra];W[sa];B[sc];W[mb]
(;B[sb];W[na]C[RIGHT];B[ra]C[RIGHT])
(;B[na];W[ma];B[sb];W[oa];B[ra]C[RIGHT]))
(;B[na];W[mb];B[ra];W[sa];B[sc];W[ma];B[sb];W[oa];B[ra]C[RIGHT])))