(;GM[1]FF[4]CA[UTF-8]AP[CGoban:2]ST[2] RU[Japanese]SZ[19]KM[0.00] PW[White]PB[Black]AW[cb][eb][bc][cc][dc][jc][cd][je]AB[fb][ec][bd][dd][ed][be][ce][de]C[This problem arose naturally from a teaching game I was watching. If you notice anything that isn't right, such as a bad move by white or a better solution to the problem, be sure to add a comment and let me know. Thanks and good luck.] (;B[ac]CR[ac] ;W[ab]CR[ab] (;B[ba]CR[ba] ;W[fa]CR[fa] (;B[ga]CR[ga] ;W[da]CR[da]C[Black can do better.]) (;B[gb]CR[gb] ;W[ca]CR[ca]C[Alive]) (;B[da]CR[da] ;W[ea]CR[ea] (;B[ga]CR[ga] ;W[db]CR[db] (;B[gb]CR[gb] ;W[ca]CR[ca]) (;B[ca]CR[ca] ;W[ad]CR[ad])) (;B[ca]CR[ca] ;W[db]CR[db]))) (;B[da]CR[da] ;W[ea]CR[ea])) (;B[ab]CR[ab] ;W[fa]CR[fa] (;B[ga]CR[ga] ;W[ea]CR[ea] ;B[gb]CR[gb] ;W[ac]CR[ac] (;B[da]CR[da] ;W[db]CR[db] ;B[ba]CR[ba] ;W[ca]CR[ca] ;B[ad]CR[ad]C[Seki is the next best thing, but black doesn't have to settle for this result.]) (;B[ba]CR[ba] ;W[ca]CR[ca] (;B[da]CR[da]C[Black can do better.]) (;B[db]CR[db]C[Black can do better.]))) (;B[gb]CR[gb] ;W[ac]CR[ac] ;B[da]CR[da] ;W[ea]CR[ea] (;B[ba]CR[ba] ;W[ca]CR[ca] ;B[ad]CR[ad]C[Seki not good enough.]) (;B[ga]CR[ga] ;W[db]CR[db] ;B[ba]CR[ba] ;W[ca]CR[ca] ;B[ad]CR[ad]C[Seki is the next best thing, but black doesn't have to settle for this result.])) (;B[da]CR[da] ;W[gb]CR[gb] ;B[fc]CR[fc] ;W[ea]CR[ea]C[Not quite good enough.])) (;B[da]CR[da] ;W[ea]CR[ea] (;B[ac]CR[ac] ;W[ab]CR[ab]C[White is alive.]) (;B[ba]CR[ba] ;W[ca]CR[ca] ;B[ab]CR[ab] ;W[ac]CR[ac] ;B[ad]CR[ad]C[Surely, black can do better.]) (;B[fa]CR[fa] ;W[db]CR[db]C[If you work out the variations, you will see white lives. Black can do much better than this.])) (;B[ea]CR[ea] ;W[da]CR[da] ;B[db]CR[db]C[Not quite. Black can give white a harder time than this.]) (;B[ba]CR[ba] ;W[fa]CR[fa] (;B[ga]CR[ga] ;W[da]CR[da] ;B[ea]CR[ea]C[RIGHT This is the best result for black and the most difficult for white; white could treat this as a two step ko and make seki, or treat it as a three step ko and make eyes. Either way, it's not easy.]) (;B[gb]CR[gb] ;W[ca]CR[ca]C[Thanks to MrMoto and BartTM for this correction.] (;B[ga]CR[ga] ;W[ea]CR[ea] (;B[db]CR[db] ;W[da]CR[da] ;B[ab]CR[ab] ;W[ac]CR[ac] ;B[ad]CR[ad]C[Black can do better.]) (;B[da]CR[da] ;W[db]CR[db] ;B[ab]CR[ab] ;W[ac]CR[ac] ;B[ad]CR[ad]C[Seki is not good enough.])) (;B[da]CR[da] ;W[ea]CR[ea]C[This will lead to seki. Black can do better.]))))