(;AB[pb]AB[qb]AB[qc]AB[rd]AB[re]AB[qe]AW[rf]AW[qf]AW[pf]AW[pe]AW[pd]AW[pc]AW[oc]AW[ob]AW[na]AB[nb]AB[nc]AB[lb]AW[se]C[White to play the best endgame without ko. White will lose every ko.]AW[rh]AP[goproblems]
(;W[rb];B[ra];W[sb];B[pa]
(;W[rc];B[oa];W[qd];B[ma]C[well doneRIGHT])
(;W[sd];B[rc];W[sc];B[oa]C[White can do better])
(;W[oa];B[rc]C[White can do better]))
(;W[sc];B[pa]
(;W[oa];B[sb]
(;W[rb];B[rc];W[sa];B[ra];W[qa]C[White will lose this ko])
(;W[ra];B[sd]C[oops])
(;W[sd];B[rc];W[sf];B[ra]C[White can do better]))
(;W[sd];B[oa]C[White can do better])
(;W[rc];B[qd]
(;W[oa];B[rb];W[sd];B[sb];W[sf];B[ra]C[White can do even better])
(;W[rb];B[oa]
(;W[sd];B[ma]C[White can do even better])
(;W[ra]C[White can do even better]))
(;W[sd];B[oa];W[rb];B[ma]C[White can do even better])))
(;W[qd];B[sc]
(;W[pa];B[rb]C[White can do better])
(;W[rb];B[ra]
(;W[pa];B[sb]C[White can do better])
(;W[sb];B[pa]C[oops]))
(;W[sf];B[pa]
(;W[oa];B[ra]C[White can do better])
(;W[sd];B[rc];W[oa];B[ra]C[White can do better])
(;W[rb];B[ra]C[White can do better])))
(;W[sd];B[sc]
(;W[sf];B[pa];W[oa];B[ra]C[];W[qd];B[rc]C[White can do better])
(;W[rb];B[sf]
(;W[se];B[ra];W[pa];B[sb]C[White can do better])
(;W[pa];B[ra];W[se];B[sb]C[White can do better])))
(;W[pa];B[qa]
(;W[oa];B[rb];W[sd];B[sc];W[sf];B[qd]C[White can do better])
(;W[rb];B[oa]C[White will lose this ko]))
(;W[qa];B[pa];W[oa];B[ra];W[sd];B[sc];W[sf];B[qd]C[White can do better])
(;W[rc];B[rb];W[sc];B[sb]C[oops])
(;W[ra];B[rb]
(;W[pa];B[qa];W[oa];B[sd]C[White can do better])
(;W[sc];B[sd]
(;W[qd];B[sf];W[pa];B[qa];W[sb];B[oa]C[life with double ko])
(;W[sb];B[qa];W[qd];B[sf];W[pa];B[oa]C[life with double ko])
(;W[pa];B[qa];W[qd];B[sf];W[sb];B[oa]C[life with double ko])))
(;W[sb];B[pa]
(;W[sd];B[oa]C[White can do better])
(;W[rc];B[rb];W[sc];B[qd];W[sd];B[oa]C[White can do better])
(;W[oa];B[sc]
(;W[rb];B[ra]C[White can do better])
(;W[sf];B[rb];W[sd];B[qd];W[rc]C[White will lose this ko]))
(;W[qd];B[sc]
(;W[sf];B[rb]C[White can do better])
(;W[rb];B[ra]C[oops])
(;W[oa];B[rb];W[sf];B[sa];W[sd];B[rc]C[White can do better])))
(;W[sa]C[NOTTHIS])
(;W[sf]C[NOTTHIS])
(;W[oa]C[NOTTHIS]))