(;AB[cc]AB[dd]AB[ed]AB[de]AB[df]AB[cf]AB[bf]AW[ec]AW[fd]AW[gc]AW[ee]AW[ef]AW[dg]AW[cg]AW[bg]AB[eg]AB[eh]AW[di]AW[dk]AW[dm]AW[cn]AW[bm]AW[do]AW[dp]AW[en]AW[fp]AW[fo]AW[go]AW[hn]AW[in]AW[jm]AW[km]AW[jj]AW[nj]AW[nk]AW[nl]AW[ol]AW[ni]AW[nh]AW[lg]AW[mg]AW[lf]AW[le]AW[kd]AW[md]AW[mc]AW[nc]AW[ob]AW[od]AW[oe]AB[id]AB[nd]AB[nf]AB[ne]AB[ng]AB[mf]AB[me]AB[of]AB[pf]AB[pc]AB[oc]AB[pb]AB[pd]AB[qc]AB[nb]AB[oh]AB[oi]AB[oj]AB[ok]AB[pl]AB[ql]AB[qm]AW[pm]AB[qp]AB[pp]AB[op]AW[qq]AW[pq]AW[nq]AW[mq]AW[kq]AW[iq]AW[hp]AB[bn]AB[co]AB[cp]AB[dq]AB[ep]AB[fq]AB[gq]AB[gp]AB[jn]AB[jo]AB[io]AB[ho]AB[jr]AB[jq]AB[im]TR[km]C[W has just played at the marked stone. If B doesn't invade the W center, he will surely lose. How should B invade?]AP[goproblems] (;B[fe];W[ff];B[ge] (;W[gf] (;B[gd];W[fc]C[Please play at AFORCE]LB[hf:A];B[hf];W[gg]LB[hg:A]C[FORCE];B[hg];W[gh]LB[hh:A]C[FORCE];B[hh];W[gi]C[FORCE] (;B[hc];W[hb];B[ib] (;W[he]C[CHOICE];B[hd];W[ie]C[FORCE] (;B[gb]C[RIGHT]) (;B[je];W[if] (;B[jg];W[jd];B[ic];W[jf];B[gb]C[RIGHT]) (;B[jf];W[ig] (;B[jg];W[ih] (;B[jh];W[ii];B[jd]C[RIGHT]) (;B[jd]C[RIGHT])) (;B[jh];W[ih];B[jg];W[ii];B[jd]C[RIGHT]) (;B[jd]C[RIGHT])) (;B[jd]C[RIGHT];W[jf];B[gb]C[RIGHT]))) (;W[ga]C[CHOICEFORCE] (;B[db];W[he];B[hd];W[ie] (;B[ia];W[jd];B[ic];W[jc]C[Please play at A]LB[eb:A];B[eb];W[jb]LB[fb:A];B[fb];W[gb]) (;B[je];W[if];B[jf];W[ig] (;B[jg];W[ih] (;B[jh];W[ii];B[jd]C[RIGHT]) (;B[jd]C[RIGHT])) (;B[jd]C[RIGHT]))) (;B[ie];W[db]C[Even though you can kill the white group, if you are looking for an even more interesting path, play C18] (;B[cb];W[fb] (;B[ia];W[ha] (;B[jc];W[kb];B[kc];W[lb];B[lc];W[mb];B[ld];W[na] (;B[ke]C[RIGHT]) (;B[jf];W[ke] (;B[ig]C[RIGHT]) (;B[jg]C[RIGHT]) (;B[jh]C[RIGHT]))) (;B[kb];W[jc];B[ic];W[jb];B[ja];W[mb] (;B[jf];W[jg];B[jd];W[kc];B[ig]C[RIGHT]) (;B[jd];W[kc];B[jf];W[jg];B[ig]C[RIGHT])) (;B[jf];W[jg] (;B[jc];W[kb];B[kc];W[lb];B[lc];W[mb];B[ld];W[na];B[ke]C[RIGHT]) (;B[kb];W[jc];B[ic];W[jb];B[ja];W[mb];B[jd];W[kc];B[ig]C[RIGHT]))) (;B[hi];W[jc] (;B[jf];W[ic];B[hd];W[jg]) (;B[jg];W[ic];B[hd];W[jf])) (;B[jf];W[jc];B[ic];W[jg];B[ig];W[je];B[jd];W[ke];B[kc];W[kb];B[jb];W[lb]) (;B[jg];W[jc];B[ic];W[jf])) (;B[fb];W[cb];B[bb];W[bd];B[bc];W[ea];B[ca])) (;B[he];W[db]C[] (;B[cb];W[fb];B[ia];W[ha] (;B[jc];W[kb];B[kc];W[lb];B[lc];W[mb];B[ld];W[na];B[ke];W[je] (;B[jd];W[jf] (;B[ie];W[jb]) (;B[jb];W[ie])) (;B[ie];W[kf] (;B[jd];W[jb]) (;B[jb];W[jd])) (;B[jb];W[kf] (;B[jd];W[ie]) (;B[ie];W[jd]))) (;B[kb];W[jc];B[ic];W[jb];B[ja];W[mb];B[jd];W[kc];B[jf];W[je];B[ie];W[jg];B[ke];W[ig])) (;B[fb];W[cb];B[bb];W[ea];B[ca]C[RIGHT])) (;B[je];W[db]C[Even though you can kill the white group, if you are looking for an even more interesting path, play C18] (;B[cb];W[fb] (;B[ia];W[ha] (;B[jc];W[kb];B[kc];W[lb];B[lc];W[mb];B[ld];W[na];B[ke]C[RIGHT]) (;B[kb];W[jc];B[ic];W[jb];B[ja];W[mb];B[jd];W[kc];B[he];W[if] (;B[jg];W[jf];B[kf];W[kg];B[ke];W[ig];B[jh];W[ih];B[ii]C[RIGHT]) (;B[jf];W[ig];B[jh]C[RIGHT])) (;B[jg];W[he];B[hd];W[jc];B[ic];W[if] (;B[ie]C[RIGHT]) (;B[jf];W[ie])) (;B[he];W[jf];B[if];W[jg] (;B[jc];W[kb];B[kc];W[lb];B[lc];W[mb];B[ld];W[na];B[ke]C[RIGHT]) (;B[kb];W[jc];B[ic];W[jb];B[ja];W[mb];B[jd]C[RIGHT]))) (;B[jg];W[jc] (;B[ic];W[he];B[hd];W[ih];B[ig];W[kf];B[jf];W[ie]) (;B[if];W[ic];B[hd]C[RIGHT]))) (;B[fb];W[cb];B[bb];W[ea] (;B[ca]C[RIGHT]) (;B[ia]C[RIGHT]) (;B[gb]C[RIGHT]))))) (;B[hd];W[ib];B[jc];W[jb];B[kc];W[mb];B[kb];W[cb];B[bb];W[db]) (;B[jc];W[hc];B[hd];W[jb];B[kb];W[ib];B[kc];W[cb] (;B[mb];W[bc]) (;B[bb];W[db];B[mb]C[RIGHT])) (;B[ic];W[hc] (;B[hd];W[ib];B[jb];W[hb];B[kc];W[db];B[cb];W[fb];B[mb]C[RIGHT]) (;B[ib];W[hd];B[he]C[RIGHT])) (;B[ib];W[hc];B[ic];W[hd];B[he]C[RIGHT]) (;B[jd];W[jb] (;B[ib];W[hb];B[ia];W[hd];B[he];W[ic];B[jc];W[hc];B[kb]C[RIGHT]) (;B[jc];W[ib];B[kc];W[mb];B[kb];W[cb] (;B[bb];W[db]) (;B[db];W[dc] (;B[hc];W[hb];B[bb];W[cd] (;B[bc];W[be]) (;B[ca];W[be])) (;B[bb];W[cd] (;B[bc];W[be]) (;B[ca];W[be])))))) (;B[he];W[hf];B[if];W[ig] (;B[hc];W[hb];B[ib];W[fb];B[ha];W[ga] (;B[gb]C[Ko. Even though W doesn't have many large threats, there is a secure way to invade.]) (;B[ia];W[cb] (;B[db];W[dc];B[bb];W[cd] (;B[ca];W[be]) (;B[bc];W[be])) (;B[bb];W[gd] (;B[hd];W[db];B[gb]C[Ko. Even though W doesn't have many large threats, there is a secure way to invade.]) (;B[gb]C[Ko. Even though W doesn't have many large threats, there is a secure way to invade.])))) (;B[gd];W[fc];B[hc];W[hb];B[ib]C[RIGHT]) (;B[hg];W[jf];B[ie];W[gg] (;B[hh];W[gh] (;B[gi];W[hi];B[ih];W[ii];B[jg];W[jh];B[ig];W[fi];B[gj];W[fh] (;B[gd];W[fc];B[hc]C[RIGHT]) (;B[hc];W[hb];B[gd];W[fc];B[ib]C[RIGHT])) (;B[ih];W[hi]C[Please play at A]LB[gi:A];B[gi];W[ii];B[jg];W[fi]C[Please play at A]LB[gj:A];B[gj];W[fh] (;B[gd];W[fc];B[hc]C[RIGHT]) (;B[hc];W[hb];B[gd];W[fc];B[ib]C[RIGHT])) (;B[hi];W[gi];B[gd];W[fc];B[hc]C[RIGHT])) (;B[gd];W[fc];B[hc]C[RIGHT])))) (;W[sa])) (;B[mb];W[ge];B[lc];W[ld];B[kc];W[jc];B[jb];W[ic]C[Not big enough]) (;B[eb];W[ge]C[Not big enough]) (;B[bo];W[ge]C[Not big enough]) (;B[db];W[fe]C[Not big enough]) (;B[om];W[ge]C[Not big enough]) (;B[ff];W[fe] (;B[gf];W[hd] (;B[he];W[ic] (;B[if];W[hh]) (;B[ie];W[gh])) (;B[gh])) (;B[fg]) (;B[gg])) (;B[gn];W[hm] (;B[fn];W[eo];B[em];W[dn];B[dl];W[cm]) (;B[gm];W[hl];B[fn];W[eo];B[em];W[dn];B[dl];W[cm])) (;B[hm];W[gn]))