( ; AB [cp][cq] AW [cn][co][dp][dq][fq] C [Can white tenuki and still kill the black stones unconditionally? Y=yes; N=no][FORCE] LB [fn:Y][gn:N] ( ; W [fn]; B [br] C [Prove it.] ( ; W [dr]; B [bo]; W [bn]; B [ap] (; W [an]; B [bs] (; W [ar]; B [aq]; W [bp]; B [bq]; W [ao] AB [cc][cd] AW [cf][ce][dd][dc][fc] ; B [be] C [You thought this was over, didn't you? Well, now you have to refute this move!] (; W [bf]; B [bc] C [Warning: Since you must go for an unconditional kill, variations where white takes the B15 stone in ko are not included.] (; W [da]; B [ba] (; W [ab]; B [ae] (; W [ac]; B [ad]; W [af] C [RIGHT][I was making this problem a few months ago, but halfway through, I thought that black could get a ko. After B5 B6 B3, I found the move D1 for white but mistakenly believed that black B1 could force a ko. Only after seeing santa c's problem 4810 did I see that white can still kill unconditionally.])(; W [af]; B [ac])(; W [cb]; B [bb])(; W [bb]; B [cb]))(; W [cb]; B [bb] (; W [ae]; B [ad] LB [af:1][ab:2][bd:3] C [Ko.])(; W [ab]; B [ad])(; W [ad]; B [ae]))(; W [ae]; B [ad] (; W [af]; B [ab])(; W [cb]; B [bb] LB [af:1][ab:2][bd:3] C [Ko.])))(; W [db]; B [ad] (; W [cb]; B [bb])(; W [bb]; B [cb] LB [ca:1][ba:2][aa:3][ab:4] C [Ko.])(; W [ba]; B [bb] LB [ab:1][ca:2][cb:3][aa:4] C [Ko.])(; W [ab]; B [ba]))(; W [cb]; B [bb] TR [db][ad])(; W [ae]; B [ad] (; W [af]; B [db])(; W [db]; B [af])(; W [cb]; B [bb] TR [af][db]))(; W [ad]; B [ae] (; W [cb]; B [bb])(; W [db]; B [ba])(; W [da]; B [ba]))) (; W [bc]; B [bb]) (; W [cb]; B [bc] TR [bb][bf]) (; W [bb]; B [bc] TR [cb][bf]) )(; W [cr]; B [bp])(; W [ao]; B [bp])(; W [bp]; B [bq] LB [ao:1][ar:2][bp:3] C [Ko.])(; W [aq]; B [ar])) (; W [cr]; B [bq]) (; W [bs]; B [bq] LB [ar:1][cs:2][cr:3][as:4] C [Ko.]) (; W [bq]; B [cr] (; W [an]; B [aq])(; W [cs]; B [bs])) ) ( ; W [bp]; B [bq] (; W [dr]; B [bo] (; W [ap] ; B [bn]; W [bm]; B [aq]; W [bs]; B [cs] (; W [as]; B [cr])(; W [cr]; B [as]))(; W [bn]; B [ap])) (; W [bn]; B [dr]) (; W [bo]; B [dr]) (; W [ao]; B [dr]) ) ) ( ; W [gn] AB [cn][co][dp][dq][fq] AW [cp][cq]; B [fn] C [The colors have changed. Live or make a ko for life.] (; W [br]; B [dr] (; W [bo]; B [bn] (; W [ap]; B [an] (; W [cr]; B [cs] (; W [bs]; B [ar] (; W [aq]; B [bp])(; W [bp]; B [aq])(; W [ao]; B [aq]))(; W [ar]; B [bs]))(; W [aq]; B [cr]; W [bs]; B [bp])(; W [bs]; B [ar]; W [aq]; B [bp])(; W [ar]; B [bs] TR [cr][cs] SQ [ao][bq]))(; W [bq]; B [ao]; W [ap]; B [an])(; W [aq]; B [bp]; W [ao]; B [cr] TR [bq][bs]))(; W [bp]; B [aq] (; W [bo]; B [bn] (; W [cr]; B [ao]; W [ap]; B [cs])(; W [cs]; B [ao]; W [ap]; B [cr])(; W [ao]; B [cr] TR [bs][ar]))(; W [cr]; B [bo]; W [ap]; W [cs])(; W [cs]; B [bo]; W [ap]; W [cr]))(; W [aq]; B [bp]; W [bo]; B [bn]; W [ao]; B [cr] TR [bq][bs])) (; W [bo]; B [bn] (; W [dr]; B [br] C [To be continued ...])(; W [bq]; B [ds] C [To be continued ...])(; W [br]; B [dr] (; W [ap]; B [an] (; W [cr]; B [cs] (; W [bs]; B [ar] (; W [aq]; B [bp])(; W [bp]; B [aq])(; W [ao]; B [aq]))(; W [ar]; B [bs]))(; W [aq]; B [cr]; W [bs]; B [bp])(; W [bs]; B [ar]; W [aq]; B [bp])(; W [ar]; B [bs] TR [cr][cs] SQ [ao][bq]))(; W [bq]; B [ao]; W [ap]; B [an])(; W [aq]; B [bp]; W [ao]; B [cr] TR [bq][bs]))(; W [bp]; B [br]; W [cr]; B [dr]; W [cs]; B [ao]; W [ar]; B [bs]; W [ap]; B [bq])(; W [ap]; B [bq] (; W [br]; B [cr]; W [bp]; B [bs])(; W [cr]; B [bp]))(; W [cr]; B [bp])) (; W [bq]; B [bo]; W [dr]; B [er] (; W [cs]; B [br]; W [ar]; B [bs])(; W [br]; B [ds])(; W [bs]; B [ds])(; W [ar]; B [cr])) (; W [bp]; B [br]; W [cr]; B [dr]; W [cs]; B [bo]; W [ar]; B [bs]; W [ap]; B [bq] C [This is not a seki because A1 is not a liberty of the large group.]) ) )