(;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]))