(;SZ[19]AW[cb]AW[ib]AW[bc]AW[dc]AW[hc]AW[jc]AW[kc]AW[lc]AW[mc]AW[nc]AW[oc]AW[bd]AW[dd]AW[hd]AW[jd]AW[od]AW[ce]AW[de]AW[he]AW[ke]AW[ne]AW[ff]AW[gf]AW[mf]AW[nf]AW[pf]AW[dg]AW[eg]AW[fg]AW[ig]AW[jg]AW[qg]AW[eh]AW[fh]AW[gh]AW[hh]AW[nh]AW[qh]AW[di]AW[ei]AW[gi]AW[ni]AW[qi]AW[ri]AW[aj]AW[bj]AW[cj]AW[ej]AW[fj]AW[mj]AW[qj]AW[bk]AW[ek]AW[jk]AW[nk]AW[ok]AW[qk]AW[bl]AW[fl]AW[gl]AW[hl]AW[il]AW[ll]AW[ml]AW[pl]AW[ql]AW[bm]AW[em]AW[gm]AW[im]AW[lm]AW[om]AW[pm]AW[gn]AW[in]AW[go]AW[qo]AW[gp]AW[pp]AW[qp]AW[rp]AW[cq]AW[dq]AW[fq]AW[gq]AW[qq]AW[dr]AW[gr]AW[pr]AW[qr]AW[sr]AW[os]AB[ic]AB[id]AB[kd]AB[ld]AB[md]AB[nd]AB[qd]AB[be]AB[ee]AB[fe]AB[ge]AB[ie]AB[je]AB[le]AB[me]AB[oe]AB[pe]AB[qe]AB[af]AB[cf]AB[df]AB[ef]AB[hf]AB[jf]AB[lf]AB[qf]AB[ag]AB[bg]AB[cg]AB[gg]AB[hg]AB[lg]AB[rg]AB[ah]AB[ch]AB[dh]AB[ih]AB[mh]AB[rh]AB[ai]AB[bi]AB[ci]AB[hi]AB[ii]AB[ki]AB[si]AB[gj]AB[lj]AB[rj]AB[ck]AB[fk]AB[gk]AB[hk]AB[ik]AB[rk]AB[cl]AB[dl]AB[el]AB[jl]AB[nl]AB[ol]AB[rl]AB[cm]AB[km]AB[mm]AB[nm]AB[cn]AB[en]AB[hn]AB[jn]AB[ln]AB[mn]AB[on]AB[pn]AB[qn]AB[rn]AB[io]AB[ko]AB[lo]AB[mo]AB[po]AB[ro]AB[bp]AB[cp]AB[dp]AB[ep]AB[fp]AB[ip]AB[jp]AB[op]AB[bq]AB[hq]AB[kq]AB[mq]AB[nq]AB[oq]AB[pq]AB[ar]AB[cr]AB[jr]AB[lr]AB[mr]AB[or]AB[bs]TR[jk]TR[gr]C[Connect the marked stones unconditionally in order to save the white group.]AB[ho]GM[1]FF[4]CA[UTF-8]AP[CGoban:2]ST[2]RU[Japanese]KM[0.00]PW[Blanc]PB[Noir]PL[W]
(;W[kk];B[jm]
(;W[ij];B[hj];W[ji]LB[kk:A]C[The stone in A was the key to solve the problemRIGHT])
(;W[ji];B[jj]
(;W[ij];B[hj];W[jh]C[RIGHT])
(;W[jh];B[kj];W[ij]C[RIGHT]))
(;W[kl];B[jj])
(;W[jj];B[kh];W[ij];B[hj];W[mg];B[lk]
(;W[mk];B[mi]
(;W[kj];B[li];W[kl];B[kg])
(;W[li];B[kj]
(;W[kl];B[lh])
(;W[lh];B[kl])))
(;W[kl];B[mi];W[li];B[kj]
(;W[mk];B[lh])
(;W[lh];B[mk]))
(;W[li];B[kj];W[kl];B[mk]))
(;W[lk];B[jj]))
(;W[jm];B[kl]
(;W[kk];B[kn]
(;W[ij];B[hj];W[ji]LB[kk:A]C[The stone in A was the key to solve the problem. This sequence was the one played in the original game. Here, black resigned.RIGHT])
(;W[ji];B[jj];W[ij];B[hj];W[jh]C[RIGHT])
(;W[jj];B[kh];W[ij];B[hj];W[lk];B[ng]
(;W[of];B[mg]
(;W[og];B[mi]MA[lh]MA[ke])
(;W[pg];B[mi]MA[lh]MA[ke])
(;W[oh];B[mi]MA[lh]MA[ke])
(;W[ph];B[mi]MA[lh]MA[ke]))
(;W[og];B[of]))
(;W[lk];B[jj]))
(;W[ij];B[hj]
(;W[ji];B[jj]
(;W[kk];B[kn]
(;W[jh]C[RIGHT])
(;W[lk];B[kj];W[mk];B[jh]))
(;W[jh];B[kk]))
(;W[jj];B[kh]
(;W[kk];B[kn];W[lk];B[ng]
(;W[of];B[mg]
(;W[og];B[mi]MA[ke]MA[lh])
(;W[pg];B[mi]MA[lh]MA[ke])
(;W[oh];B[mi]MA[lh]MA[ke])
(;W[ph];B[mi]MA[lh]MA[ke]))
(;W[og];B[of]))
(;W[lk];B[kk])
(;W[kj];B[ji]))
(;W[kk];B[kn]
(;W[ji]C[RIGHT])
(;W[jj];B[kh];W[lk];B[ng]
(;W[of];B[mg]
(;W[og];B[mi]MA[ke]MA[lh])
(;W[pg];B[mi]MA[lh]MA[ke])
(;W[oh];B[mi]MA[lh]MA[ke])
(;W[ph];B[mi]MA[lh]MA[ke]))
(;W[og];B[of]))))
(;W[jj];B[kh];W[ij];B[hj];W[kk];B[kn];W[lk];B[ng]
(;W[of];B[mg]
(;W[og];B[mi]MA[lh]MA[ke])
(;W[pg];B[mi]MA[ke]MA[lh])
(;W[oh];B[mi]MA[lh]MA[ke])
(;W[ph];B[mi]MA[lh]MA[ke]))
(;W[og];B[of]))
(;W[ji];B[jj];W[kk];B[kn]
(;W[ij]C[RIGHT];B[hj];W[jh]C[RIGHT])
(;W[jh];B[kj];W[ij];B[lk])
(;W[lk];B[jh])))
(;W[ij];B[hj]
(;W[ji];B[jj]
(;W[kk];B[jm]
(;W[jh]LB[kk:A]C[The stone in A was the key to solve the problemRIGHT])
(;W[kj];B[jh]))
(;W[jm];B[kk];W[kl];B[jk]C[this is a ko .. can do better])
(;W[jh];B[kk]))
(;W[jm]PL[W];B[kl]
(;W[kk];B[kn];W[ji]LB[kk:A]C[The stone in A was the key to solve the problemRIGHT])
(;W[ji];B[jj];W[kk];B[kn]
(;W[jh]C[RIGHT])
(;W[lk];B[kj];W[mk];B[jh])))
(;W[kk];B[jm];W[ji]LB[kk:A]C[The stone in A was the key to solve the problemRIGHT])
(;W[jj];B[kh]
(;W[kk];B[kl];W[lk];B[ng]
(;W[og];B[of])
(;W[of];B[mg]
(;W[og];B[li]MA[lh]MA[ke])
(;W[pg];B[li]MA[ke]MA[lh])))
(;W[kl];B[jm];W[kk];B[mi]MA[lh]MA[ke])
(;W[kj];B[kk])
(;W[lk];B[kk];W[kj];B[li];W[kl];B[jm]
(;W[mk];B[kg]MA[ke]MA[lh])
(;W[kk];B[kg]MA[ke]MA[lh])))
(;W[kj];B[jj];W[kk];B[lk]))
(;W[jj];B[kh];W[ij];B[hj];W[kk];B[kl];W[lk];B[mi]MA[lh]MA[ke])
(;W[ji];B[jj];W[kk];B[jm]
(;W[ij];B[hj];W[jh]C[RIGHT])
(;W[jh];B[kj];W[ij]C[RIGHT]))
(;W[hj];B[ij])
(;W[kl];B[jm]
(;W[ij];B[hj];W[jj];B[kh]
(;W[kk];B[mi])
(;W[kj];B[ji];W[kk];B[mk]))
(;W[jj];B[kh];W[ij];B[hj]
(;W[kk];B[mi])
(;W[kj];B[ji];W[kk];B[mk]))
(;W[ji];B[jj]
(;W[kk];B[jh])
(;W[jh];B[kk]))
(;W[kj];B[jj];W[kk];B[mk])
(;W[kk];B[jj]MA[hj]MA[ke]))
(;W[kj];B[jj]
(;W[jm];B[kl])
(;W[kk];B[lk])
(;W[kl];B[jm];W[kk];B[mk])))