(;SZ[13]AW[ei]AW[fi]AW[dj]AW[ej]AW[bk]AW[ck]AW[ek]AW[gk]AW[hk]AW[bl]AW[dl]AW[il]AB[af]AB[cf]AB[df]AB[ef]AB[ff]AB[bg]AB[cg]AB[gg]AB[fh]AB[bi]AB[ci]AB[gi]AB[cj]AB[fj]AB[gj]AB[hj]AB[fk]AB[el]AB[gl]AB[fm]TR[ci]C[Black to play and kill White. White could live if not for the marked stone.]PW[White]PB[Black] (;B[cm];W[dm] (;B[ak];W[aj] (;B[bj] (;W[al]C[CHOICE] (;B[bm]C[White only has one real eye. Good job.RIGHT]) (;B[ai];W[bm])) (;W[bm]C[CHOICE] (;B[al];W[am];B[ak]C[White only has one real eye. Good job.RIGHT]) (;B[am];W[al]) (;B[ai];W[al]) (;B[em];W[al]) (;B[di];W[al]) (;B[eh];W[al]))) (;B[bm];W[bj] (;B[am];W[al]) (;B[al];W[cl])) (;B[ai];W[bj];B[bm];W[al]) (;B[am];W[bj]) (;B[al];W[am] (;B[ak];W[bj]) (;B[bm];W[bj];B[al];W[cl] (;B[am];W[ak];B[bm];W[am];B[al];W[cm]C[The bent four in the corner only works if White has no outside liberties.]) (;B[ai];W[ak]) (;B[di];W[ak]) (;B[em];W[ak]) (;B[eh];W[ak])))) (;B[bm] (;W[am]C[CHOICE] (;B[ak];W[aj] (;B[bj]C[White only has one real eye. Good job.RIGHT]) (;B[al];W[bj]) (;B[ai];W[bj])) (;B[aj];W[ak];B[al];W[cl]) (;B[al];W[ak] (;B[am];W[cl];B[bm];W[am];B[al];W[cm]C[The bent four in the corner only works if White has no outside liberties.]) (;B[aj];W[cl]) (;B[bj];W[cl]) (;B[di];W[cl]) (;B[eh];W[cl]) (;B[em];W[cl]))) (;W[bj]C[CHOICE] (;B[aj] (;W[ak]C[CHOICE] (;B[ai];W[am];B[al];W[cl]) (;B[am]C[Black makes a 3-point nakade. At the end of the game, White will have no outside liberties and Black can make bent four in the corner. See problem 6560. Good job.RIGHT]) (;B[al];W[am])) (;W[am]C[CHOICE] (;B[ak]C[White only has one real eye. Good job.RIGHT]) (;B[al];W[ak] (;B[am];W[cl];B[bm];W[am];B[al];W[cm]C[The bent four in the corner only works if White has no outside liberties.]) (;B[ai];W[cl]) (;B[em];W[am]C[Imagine A is a ko threat bigger than this group.]LB[if:A];B[if];W[ig]C[White answers.];B[al];W[ai]C[Black can never win the ko in the corner because Black would need to simultaneously win the ko above it.]) (;B[di];W[cl]) (;B[eh];W[cl])))) (;B[am];W[aj];B[al];W[cl] (;B[eh];W[ak];B[bm];W[am];B[al];W[cm]C[The bent four in the corner only works if White has no outside liberties.]) (;B[di];W[ak];B[bm];W[am];B[al];W[cm]C[The bent four in the corner only works if White has no outside liberties.]) (;B[ai];W[ak];B[bm];W[am];B[al];W[cm]C[The bent four in the corner only works if White has no outside liberties.]) (;B[em];W[ak];B[bm];W[am];B[al];W[cm]C[The bent four in the corner only works if White has no outside liberties.])) (;B[al];W[aj] (;B[ai];W[cl];B[am];W[ak];B[bm];W[am];B[al];W[cm]C[The bent four in the corner only works if White has no outside liberties.]) (;B[em];W[cl];B[am];W[ak];B[bm];W[am];B[al];W[cm]C[The bent four in the corner only works if White has no outside liberties.]) (;B[di];W[cl];B[am];W[ak];B[bm];W[am];B[al];W[cm]C[The bent four in the corner only works if White has no outside liberties.]) (;B[eh];W[cl];B[am];W[ak];B[bm];W[am];B[al];W[cm]C[The bent four in the corner only works if White has no outside liberties.]) (;B[am];W[cl] (;B[ai];W[ak];B[bm];W[am];B[al];W[cm]C[The bent four in the corner only works if White has no outside liberties.]) (;B[di];W[ak];B[bm];W[am];B[al];W[cm]C[The bent four in the corner only works if White has no outside liberties.]) (;B[eh];W[ak];B[bm];W[am];B[al];W[cm]C[The bent four in the corner only works if White has no outside liberties.]) (;B[em];W[ak];B[bm];W[am];B[al];W[cm]C[The bent four in the corner only works if White has no outside liberties.]))))) (;B[al];W[ak];B[bm];W[am]) (;B[aj];W[ak];B[bm];W[am];B[al];W[cl]) (;B[am];W[bm])) (;B[ak];W[cm] (;B[al];W[aj]) (;B[am];W[al]) (;B[bj];W[al])) (;B[aj];W[cm]) (;B[dm];W[cm] (;B[ak];W[aj] (;B[bj];W[al]) (;B[ai];W[bj]) (;B[al];W[am])) (;B[al];W[ak])) (;B[al];W[cm];B[ak];W[aj]) (;B[di];W[cm]) (;B[eh];W[cm]) (;B[bm];W[cm]) (;B[am];W[cm]) (;B[bj];W[cm]) (;B[em];W[cm]) (;B[cl];W[cm]))