(;AB[bo]AB[ap]AB[bq]AB[cq]AB[ar]AB[cr]AB[ds]AB[er]AB[fq]AB[gp]AB[fo]AB[en]AB[dm]AB[gr]AB[cs]AB[fn]AB[bl]AB[ck]AW[br]AW[as]AW[bp]AW[cp]AW[cn]AW[bn]AW[do]AW[eo]AW[ep]AW[eq]AW[dq]AW[dr]AW[ao]MA[ao]C[Problem 13109 ends in ko. Desperate for a ko threat, White plays A5. Now what?]AW[fp]AP[goproblems] (;B[an] (;W[aq]LB[ek:T]C[White takes the ko. Play at E9 (T) if you need a ko threat. Though quite big it is not as valuable as the whole group.] (;B[ao];W[am] (;B[bm];W[co] (;B[ao]MA[ap]MA[an]C[White is dead! White A5 was not a real ko threat after all.RIGHT]) (;B[al];W[an]) (;B[an];W[ao]) (;B[ap];W[ao]) (;B[bs];W[es])) (;B[ar];W[fr]C[White plays an internal ko threat...] (;B[bs];W[gq]C[White escapes.]) (;B[fs];W[aq]C[White retakes the ko. Play at E9 (T) for a ko threat that is worth less than the whole group.]LB[ek:T] (;B[ek];W[co]C[White ignores your threat and lives. You could have killed White without using the threat...]) (;B[bm];W[co] (;B[ao]C[White is dead!RIGHT]MA[an]MA[ap]) (;B[al];W[an]) (;B[ap];W[ao]) (;B[an];W[ao]) (;B[bs];W[es])) (;B[bs];W[es]) (;B[al];W[co]) (;B[cm];W[co]) (;B[dn];W[co])) (;B[gq];W[aq]C[White retakes the ko. Play at E9 (T) for a ko threat that is worth less than the whole group.]LB[ek:T];B[bm];W[co] (;B[ao]C[];W[es]) (;B[fs];W[an])) (;B[es];W[aq]C[White retakes the ko. Play at E9 (T) for a ko threat that is worth less than the whole group.]LB[ek:T] (;B[ek];W[co]) (;B[bm];W[co] (;B[ao];W[gq]C[White escapes]) (;B[fs];W[an]) (;B[gq];W[an])) (;B[fs];W[co])) (;B[bm];W[gq]C[White escapes]) (;B[aq];W[gq]C[White escapes]) (;B[dn];W[gq]C[White escapes]) (;B[cm];W[gq]C[White escapes]) (;B[al];W[gq]C[White escapes])) (;B[al];W[co]) (;B[bs];W[es]) (;B[cm];W[co]) (;B[dn];W[co]) (;B[es];W[co])) (;B[ek];W[am]C[White ignores the threat...] (;B[ao];W[co]C[White lives while you could have killed unconditionally.]) (;B[bm];W[ao]C[White lives while you could have killed unconditionally.]) (;B[ar];W[co]MA[bo]MA[an]C[White lives!])) (;B[am];W[ao]C[White gets a ko]) (;B[bm];W[ao]C[Ko for White]) (;B[bs];W[es]) (;B[co];W[ao]) (;B[dn];W[am] (;B[ar];W[co]C[White lives.]) (;B[ao];W[co]) (;B[bm];W[ao])) (;B[cm];W[am] (;B[ao];W[co]) (;B[ar];W[co]MA[bo]MA[an]C[White lives.]) (;B[bm];W[ao]))) (;W[am];B[ao];W[aq];B[bm];W[co] (;B[ao]MA[ap]MA[an]C[White is dead! White A5 was not a real ko threat after all.RIGHT]) (;B[al];W[an]) (;B[an];W[ao]) (;B[ap];W[ao]) (;B[bs];W[es]))) (;B[bs];W[an]C[White lives.]) (;B[aq];W[an]C[White is alive.]) (;B[es];W[aq]) (;B[am];W[aq]) (;B[dn];W[aq]) (;B[bm];W[aq]) (;B[cm];W[aq]))