(;AB[pq]AB[qq]AB[rq]AB[op]AB[np]AB[nq]AB[nr]AW[or]AW[oq]AW[pr]AW[oo]AW[pp]AW[qp]AW[rp]AW[so]AW[sq]AB[rr]AB[jp]AW[rn]C[Try to kill Black unconditionally.]AP[goproblems]
(;W[qs]
(;B[sr]
(;W[sp]C[Black dies. This move may seem unimportant, but otherwise the ko gives Black an extra liberty; then White cannot give atari from below because of a shortage of liberties.RIGHT])
(;W[rs];B[sp]
(;W[ss];B[os]
(;W[sq]C[Only ko. Even though Black has to neglect 2 ko threats to save the group, this is a failure for White as Black could have been killed outright.])
(;W[qr];B[ps])
(;W[ps];B[qr])
(;W[ns];B[ms]
(;W[sq]C[Only ko. Black has to find the first ko threat and neglect 2 White ko threats to save the group; still this is a failure for White as Black could have been killed outright.])
(;W[ps];B[qr])
(;W[qr];B[ps])))
(;W[qr];B[os];W[sq]C[Only ko. Black has to find the first ko threat and neglect 2 White ko threats to save the group; still this is a failure for White as Black could have been killed outright.])
(;W[sq]C[Only ko. This is a failure for White as Black could have been killed outright.])
(;W[os];B[qr]
(;W[sq]C[Ko])
(;W[ss];B[ps])
(;W[ps];B[ns])
(;W[ns];B[ms])
(;W[ro];B[ns]))
(;W[ps];B[ns]
(;W[sq]C[Ko (Black is alive in seki - at least!)])
(;W[qr];B[os])
(;W[ss];B[os])
(;W[os];B[ss])
(;W[ro];B[os]
(;W[ss];B[qr])
(;W[qr];B[ss])
(;W[sq]C[Ko; Black gets a life in seki - at least!])))
(;W[ns];B[ms]
(;W[ps];B[os]C[Ko; if Black wins it Black is alive in seki - at least!])
(;W[os];B[qr])
(;W[qr];B[os]
(;W[sq]C[Only ko. Black has to find the first ko threat and neglect 2 White ko threats to save the group; still this is a failure for White as Black could have been killed outright.])
(;W[ps];B[ss])
(;W[ss];B[ps]))
(;W[ss];B[os]
(;W[sq]C[Only ko. Black has to find the first ko threat and neglect 2 White ko threats to save the group; still this is a failure for White as Black could have been killed outright.])
(;W[ps];B[qr])
(;W[qr];B[ps]))
(;W[sq]C[Only ko. This is a failure for White as Black could have been killed outright.])))
(;W[qr];B[sp]
(;W[rs];B[os];W[sq]C[Only ko. Black has to find the first ko threat and neglect 2 White ko threats to save the group; still this is a failure for White as Black could have been killed outright.])
(;W[sq]C[Ko])
(;W[os];B[rs]
(;W[ns];B[ms])
(;W[sq]C[Only ko. Black has to find the first ko threat to save the group; still this is a failure for White as Black could have been killed outright.]))
(;W[ps];B[rs])
(;W[ss];B[os]
(;W[sq]C[Only ko. Black has to find the first ko threat to save the group; still this is a failure for White as Black could have been killed outright.])
(;W[rs];B[ps])
(;W[ps];B[rs]))
(;W[ns];B[ms]
(;W[sq]C[Only ko. This is a failure for White as Black could have been killed outright.])
(;W[os];B[rs])
(;W[rs];B[os]
(;W[sq]C[Only ko. Black has to find the first ko threat and neglect 2 White ko threats to save the group; still this is a failure for White as Black could have been killed outright.])
(;W[ps];B[ss])
(;W[ss]))
(;W[ss];B[os]C[]
(;W[sq]C[Only ko. Black has to find the first ko threat; still this is a failure for White as Black could have been killed outright.])
(;W[rs];B[ps])
(;W[ps];B[rs]))
(;W[ps];B[rs])))
(;W[os];B[qr]
(;W[sp];B[ns])
(;W[rs];B[sp]C[Ko])
(;W[ss];B[sp]C[Ko])
(;W[ps];B[ns])
(;W[ns];B[ms]))
(;W[ps];B[rs])
(;W[ss];B[rs]
(;W[qr];B[sp]C[Ko])
(;W[sp];B[os])
(;W[os];B[sp]C[Ko, Black can get seki at least.])))
(;B[rs]
(;W[sr];B[os]
(;W[sp];B[ns]
(;W[ss]C[RIGHT])
(;W[qr];B[ps]))
(;W[qr];B[ps])
(;W[ss];B[sp])
(;W[ps];B[qr]))
(;W[qr];B[os])
(;W[os];B[qr]
(;W[sr];B[ps]C[Ko])
(;W[ss];B[ps]C[Ko])
(;W[sp];B[ns])
(;W[ns];B[ms]))
(;W[ss];B[sr]
(;W[qr];B[sp]C[Ko])
(;W[sp];B[os])
(;W[os];B[sp]C[Ko, Black can get seki at least.]))
(;W[ps];B[qr])
(;W[ns];B[qr]
(;W[sr];B[ps])
(;W[ss];B[ps])
(;W[ps];B[os])
(;W[os];B[ms])
(;W[ms];B[os]))
(;W[sp];B[qr]
(;W[os];B[ns])
(;W[ps];B[os])
(;W[sr];B[ps])
(;W[ss];B[ps])
(;W[ns];B[os]
(;W[ps];B[os])
(;W[ms];B[ps])
(;W[sr];B[ps])
(;W[ss];B[ps]))))
(;B[os]
(;W[rs];B[sr]
(;W[sp]C[RIGHT])
(;W[qr];B[sp]C[Ko])
(;W[ss];B[sp]C[Ko])
(;W[ps];B[ns]
(;W[sp]C[Gote seki])
(;W[qr];B[ss])
(;W[ss];B[qr])))
(;W[sr];B[rs]
(;W[sp];B[ns]
(;W[ss]C[RIGHT])
(;W[qr];B[ps]))
(;W[qr];B[ps])
(;W[ss];B[sp])
(;W[ps];B[qr]))
(;W[qr];B[rs])
(;W[ps];B[rs]
(;W[ns];B[qr])
(;W[sr];B[qr])
(;W[ss];B[qr]))
(;W[ns];B[qr])
(;W[ss];B[qr])))
(;W[rs];B[qs]
(;W[sr];B[ss]C[To keep this problem simple you don't need an external ko threat if you want to fight the ko; you can take it right back.]
(;W[qr];B[sp])
(;W[sp];B[os];W[rs]C[Ko.])
(;W[rs]C[Only ko. This is a failure for White as Black could have been killed outright.])
(;W[ps];B[sp])
(;W[os];B[sp])
(;W[ns];B[sp]
(;W[mr];B[os]
(;W[ps];B[qr])
(;W[sq];B[ms]))
(;W[ms];B[os]
(;W[ps];B[qr])
(;W[sq];B[ps]))
(;W[os];B[lr])
(;W[sq];B[ms])))
(;W[qr];B[ss]
(;W[sr];B[sp])
(;W[sp];B[os])
(;W[ps];B[os])
(;W[os];B[ns])
(;W[ns];B[ps]))
(;W[ps];B[ss]
(;W[sp];B[qr])
(;W[qr];B[os])
(;W[sr];B[sp]))
(;W[os];B[ss])
(;W[ss];B[sr])
(;W[ns];B[qr]
(;W[sr];B[ss]C[Only ko.])
(;W[os];B[ms])
(;W[ps];B[os])
(;W[ms];B[os])
(;W[ss];B[sr])
(;W[mr];B[os])))
(;W[sr];B[qs]
(;W[qr];B[rs]
(;W[sp];B[os])
(;W[os];B[ns])
(;W[ps];B[os])
(;W[ss];B[sp])
(;W[ns];B[ps]))
(;W[ps];B[ns]
(;W[rs];B[ss]C[Ko])
(;W[ss];B[os])
(;W[os];B[qr])
(;W[qr];B[os])
(;W[sp];B[os]))
(;W[os]
(;B[ns];W[rs];B[ss]C[Ko (and Black could have had a seki as well)])
(;B[rs];W[sp];B[ns];W[ss]C[Gote seki]))
(;W[rs];B[ss]C[Only ko. This is a failure for White as Black could have been killed outright.]
(;W[qr];B[sp])
(;W[sp];B[os];W[rs]C[Ko.])
(;W[rs]C[Only ko. This is a failure for White as Black could have been killed outright.])
(;W[ps];B[sp])
(;W[os];B[sp])
(;W[ns];B[sp]
(;W[mr];B[os]
(;W[ps];B[qr])
(;W[sq];B[ms]))
(;W[ms];B[os]
(;W[ps];B[qr])
(;W[sq];B[ps]))
(;W[os];B[lr])
(;W[sq];B[ms])))
(;W[ss];B[os]
(;W[rs];B[sp])
(;W[qr];B[ps])
(;W[ps];B[qr])
(;W[sp];B[ps]))
(;W[sp];B[os]
(;W[rs];B[ss]C[Ko])
(;W[ss];B[ps])))
(;W[qr]
(;B[qs]
(;W[sr];B[rs]
(;W[sp];B[os])
(;W[os];B[ns])
(;W[ps];B[os])
(;W[ss];B[sp])
(;W[ns];B[ps]))
(;W[rs];B[ss]
(;W[sr])
(;W[sp];B[os])
(;W[ps];B[os])
(;W[os];B[ns])
(;W[ns];B[ps]))
(;W[os];B[ns])
(;W[ss];B[os])
(;W[ps];B[os])
(;W[ns];B[ps]))
(;B[rs]
(;W[sr];B[os])
(;W[qs];B[os])
(;W[ss];B[os])
(;W[ps];B[sr])
(;W[os];B[ns])
(;W[ns];B[qs])))
(;W[ss];B[qr]
(;W[sr];B[os])
(;W[rs];B[os])
(;W[qs];B[os])
(;W[ps];B[qs]))
(;W[ps];B[qs]
(;W[sr];B[ns]
(;W[rs];B[ss]C[Ko])
(;W[ss];B[os])
(;W[os];B[qr])
(;W[qr];B[os])
(;W[sp];B[os]))
(;W[rs];B[ss]
(;W[sp];B[qr])
(;W[qr])
(;W[sr]))
(;W[ss];B[qr])
(;W[sp];B[qr]))
(;W[os];B[qr])
(;W[ns];B[qr]
(;W[sr];B[ps])
(;W[os];B[ms])
(;W[ms];B[os];W[ps];B[qs];W[os];B[ls];W[mr];B[lr];W[mq];B[mp];W[lq];B[kq];W[lp];B[lo])
(;W[qs];B[ps];W[os];B[ms])
(;W[ps];B[qs]))
(;W[sp];B[qr]))
BartTM