(;AB[sr]AB[rr]AB[pr]AB[ps]AW[qr]AW[qs]AW[rs]AW[rq]AW[sp]AW[so]AW[rn]AW[qn]AW[pn]AW[oo]AW[pp]AB[po]AB[op]AB[oq]AB[or]AW[lr]AW[ls]AW[mr]AB[os]AB[ns]AB[nq]AB[mq]AB[lq]AW[no]AB[np]AB[on]AB[om]AB[pm]AB[qm]AB[rm]AB[sm]AW[mp]AW[lp]AW[kp]AW[jq]AW[ip]AW[hq]AW[gr]AW[fq]AB[jr]AB[js]AB[is]AW[lm]C[Do not waste internal ko-treats during the solution; only play on X when you need a suitable ko-threat.]LB[mo:X]AP[goproblems] (;B[qq] (;W[qp] (;B[ss] (;W[qs] (;B[kq] (;W[kr] (;B[ir] (;W[qr] (;B[rs] (;W[qr] (;B[pq] (;W[iq] (;B[rp];W[ro] (;B[sq] (;W[qs];B[rr] (;W[rs] (;B[ss] (;W[sq]C[CHOICE] (;B[qs];W[sr] (;B[ms];W[rs]C[Please play the natural internal ko-treat on XFORCE]LB[mo:X];B[mo];W[nn];B[ss]C[RIGHT] (;W[fm]C[White plays an external ko threat. Ignore it.RIGHT];B[ks]C[RIGHT] (;W[gm]C[White cashes in on the koCHOICERIGHT];B[rs]C[RIGHT];W[hm]C[And white takes sente to complete his one-step-ko profit. Black is happy to save over 60 points.RIGHT]) (;W[rs]C[CHOICERIGHT];B[nr]C[RIGHT];W[lr]C[RIGHT];B[ss]C[RIGHT];W[gm]C[White plays an external ko threat. Ignore it.RIGHT];B[rs]C[And white takes sente to complete his one-step-ko profit. Black is happy to save over 60 points.RIGHT])) (;W[hr]C[This path is for information only; the computer will not play itRIGHT];B[nr]C[RIGHT];W[rs]C[RIGHT];B[ks]C[RIGHT];W[lr]C[RIGHT];B[ss]C[This is just a direct ko for White.RIGHT])) (;B[nr]C[NOTTHIS]) (;B[ks];W[hr])) (;B[ms];W[qs] (;B[ks];W[sr] (;B[qr];W[rs];B[ss];W[rs]) (;B[nr];W[lr];B[qr];W[rs];B[ss];W[rs])) (;B[rs];W[sr];B[qr];W[hr]) (;B[sr];W[hr]) (;B[qr];W[sr];B[rs];W[hr])) (;B[nr]C[NOTTHIS]) (;B[ks];W[hr])) (;W[qs]C[CHOICE] (;B[sq];W[sr]C[Please play the natural ko-threat on XFORCE]LB[mo:X];B[mo];W[nn];B[sq]C[RIGHT];W[qo]C[Please capture the koFORCERIGHT];B[rp]C[RIGHT] (;W[hr]C[Please connect for 2 eyesCHOICEFORCERIGHT];B[rq]C[RIGHT];W[hs]C[CHOICERIGHT]) (;W[nm]C[Please connect for 2 eyesCHOICEFORCERIGHT];B[rq]C[RIGHT])) (;B[nr]C[NOTTHIS]) (;B[ms];W[sq] (;B[ks];W[sr] (;B[qr];W[rs];B[ss];W[rs]) (;B[nr];W[lr];B[qr];W[rs];B[ss];W[rs])) (;B[rs];W[sr];B[qr];W[hr]) (;B[sr];W[hr]) (;B[qr];W[sr];B[rs])) (;B[rs];W[sq] (;B[ms];W[sr];B[qr];W[hr]) (;B[nr]C[NOTTHIS]) (;B[qr];W[sr] (;B[nr]C[NOTTHIS]) (;B[ms];W[hr]))))) (;B[sr];W[hr];B[ss];W[qs] (;B[sq];W[hs];B[rp];W[qo]C[Black has no tricks left]) (;B[qr];W[sq]) (;B[ms];W[sq]) (;B[nr]C[NOTTHIS]))) (;W[hr]C[This path is for information only; the computer will not play it];B[rs] (;W[sr];B[ms];W[qr];B[qs];W[hs];B[nr];W[ks];B[jr]C[RIGHT]) (;W[hs];B[sr]C[RIGHT]))) (;W[hr]C[This path is for information only; the computer will not play it];B[rp];W[qo];B[nr];W[rq];B[fm]C[Black must play an external ko threat];W[fn];B[rp] (;W[hs];B[ms];W[ks];B[jr];W[rq];B[js]C[RIGHT]) (;W[gn]C[White can also play an external ko-threat];B[ms];W[rq];B[ks];W[qs];B[rr]C[RIGHT])) (;W[rp];B[sn];W[qs];B[rr]C[This is not as good for white as the main variation. Compare for yourself.RIGHT])) (;B[ms];W[hr];B[sq];W[qs];B[rr];W[nr]) (;B[nr]C[NOTTHIS]) (;B[qs];W[sq] (;B[ms];W[hr];B[nr];W[qr]) (;B[nr]C[NOTTHIS]))) (;B[sq];W[rp] (;B[ms];W[hr]) (;B[nr]C[NOTTHIS]) (;B[qo]C[NOTTHIS])) (;B[ms];W[hr] (;B[qs];W[sq]) (;B[rp];W[ro];B[sq];W[qs];B[rr];W[nr]))) (;W[sq]C[This path is for information only; the computer will not play it];B[ks] (;W[iq];B[ms];W[qs];B[nr] (;W[lr];B[rr]C[RIGHT]) (;W[rr];B[lr]C[Not even a ko for whiteRIGHT])) (;W[qs];B[rr] (;W[iq];B[rs] (;W[sr];B[ms]C[RIGHT]) (;W[hr];B[sr]C[RIGHT])) (;W[rs];B[ss];W[qs];B[rs];W[sr];B[qr];W[iq];B[ms]C[RIGHT])))) (;B[qs] (;W[sq] (;B[pq];W[iq] (;B[ms];W[hr]) (;B[nr]C[NOTTHIS]) (;B[ks];W[hr])) (;B[ms];W[pq]) (;B[nr]C[NOTTHIS])) (;W[pq]C[This is not such a good idea for white];B[rp];W[ro];B[sq]C[This gives Black a fighting chance that he shouldn't have in this line.RIGHT]))) (;W[pq]C[This path is for information only; the computer will not play it];B[qr];W[iq];B[ms];W[hr];B[nr]C[RIGHT]) (;W[sq];B[qr]C[];W[iq];B[ms];W[pq];B[ks]C[RIGHT])) (;B[pq];W[iq];B[rs];W[hr];B[ms];W[qr] (;B[qs];W[sq]) (;B[rp];W[ro];B[sq];W[qs];B[rr];W[nr]))) (;W[iq]C[This path is for information only; the computer will not play it] (;B[qr];W[hr] (;B[ms];W[hs];B[nr];W[ks];B[jr]C[RIGHT]) (;B[nr]C[Of course, this move also works, but the main line is given as an example since the computer will not play this variation!NOTTHISRIGHT])) (;B[ms]C[This is a mistake];W[qr];B[rs];W[qr];B[pq];W[hr] (;B[qs];W[sq]) (;B[rp];W[ro];B[sq];W[qs];B[rr];W[nr])))) (;B[hr];W[iq]C[You neither gained a liberty nor a good shape. Compare to the correct solution.]) (;B[ms];W[qr];B[rs];W[qr];B[pq];W[ir];B[qs];W[sq]) (;B[nr]C[NOTTHIS]) (;B[qr] (;W[pq];B[nr];W[sq];B[ks]) (;W[ir];B[ms];W[hs];B[nr];W[ks]))) (;W[qr]C[This path is for information only; the computer will not play it];B[kr] (;W[ms];B[rs]C[Excellent for BlackRIGHT]) (;W[pq];B[ms]C[SekiRIGHT]))) (;B[kr];W[kq] (;B[qr];W[ir]) (;B[ir];W[iq] (;B[qr];W[hr]) (;B[ms];W[qr] (;B[rs];W[qr] (;B[qs];W[sq];B[pq];W[hr]) (;B[pq];W[hr];B[rp];W[ro];B[sq];W[qs];B[rr];W[nr])) (;B[pq];W[hr];B[rs];W[hs])) (;B[nr]C[NOTTHIS])) (;B[ms];W[qr] (;B[rs];W[qr] (;B[qs];W[sq];B[pq];W[ir]) (;B[pq];W[ir];B[rp];W[ro] (;B[sq];W[qs];B[rr];W[nr]) (;B[qs];W[sq];B[nr];W[qr]))) (;B[pq];W[ir];B[rs];W[hs])) (;B[ks];W[ir];B[nr];W[hs]C[This won't help either for Black])) (;B[rp];W[kq]C[There is just one eye on the right side and none on the left]) (;B[qr];W[kq];B[kr];W[ir]) (;B[pq];W[kq];B[kr];W[ir];B[rp];W[ro];B[sq];W[mn])) (;W[pq]C[This path is for information only; the computer will not play it] (;B[qs];W[qr]C[];B[mo];W[nn];B[qq] (;W[kq];B[rp];W[qr];B[nm];W[mn];B[qq];W[ro];B[sq];W[qr];B[mm];W[ln];B[qq];W[rp];B[sn];W[qr];B[fm];W[fn];B[qq];W[gn];B[qo]C[RIGHT]) (;W[sq];B[kq] (;W[qr];B[kr];W[ms];B[qq]C[Good result for black with several internal ko threats remainingRIGHT]) (;W[kr];B[ms];W[qr];B[nm];W[mn];B[qq] (;W[ir];B[nr];W[qr];B[ks];W[lr];B[qq]C[A direct ko is very good for blackRIGHT]) (;W[fm]C[White plays an external ko-threat];B[ks];W[gm];B[qr]C[RIGHT];W[hm]C[Blackb saves 60 points in exchange for a one-step-koRIGHT])))) (;B[qr];W[kq];B[kr];W[ir]) (;B[kq];W[qr]C[Black is dead]))) (;B[pq];W[kq] (;B[ss];W[qs] (;B[rp];W[ro];B[sq];W[qo]) (;B[kr];W[ir];B[rp];W[ro];B[sq];W[mn])) (;B[kr];W[ir];B[ss];W[qs];B[rp];W[ro];B[sq];W[mn])) (;B[rp];W[pq]) (;B[kr];W[pq] (;B[ms];W[kq]) (;B[kq];W[ms]))) (;W[kq]C[This path is for information only; the computer will not play it];B[qp];W[qo];B[rp];W[sq];B[sn];W[ss];B[pq];W[po];B[rr];W[ro];B[sr]C[RIGHT])) (;B[kq];W[pq] (;B[kr];W[ms]) (;B[ms];W[kr])) (;B[qp];W[qq];B[pq];W[kq]C[Now first play at X please]LB[kr:X] (;B[kr];W[ir] (;B[sn];W[ro];B[rp];W[nr]C[White's eye wins]) (;B[ro];W[sn];B[rp];W[nr]C[White's eye wins]) (;B[rp];W[nr]C[White's eye wins])) (;B[sn]C[NOTTHIS]) (;B[rp]C[NOTTHIS]) (;B[ro]C[NOTTHIS])) (;B[kr];W[pq] (;B[ms];W[kq]) (;B[kq];W[ms])))