Problem 10874 goproblems.com


Author	BartTM	Created	2008-02-08
Difficulty	8 dan (history)	Source	Problem 10786 & countless hours of research
AVG solve time	108 sec	Stars	4.5 (2 votes)
User attempts	38 / 331	Collections	N/A
Genre	life and death	Your attempts	N/A
Similar problems
Created	2008-02-08
Source	Problem 10786 & countless hours of research
Stars	4.5 (2 votes)
Collections	N/A
Your attempts	N/A

(;AW[sr]AW[sq]AW[rq]AW[rp]AW[so]AW[qo]AW[po]AW[pp]AW[oo]AW[mp]AW[lp]AW[lq]AW[kq]AW[kr]AW[np]AB[rr]AB[qr]AB[qq]AB[qp]AB[oq]AB[op]AB[nq]AB[mq]AB[mr]AB[lr]C[The marked move is wrong, but what is the best way to prove it?]AW[ns]AW[ir]TR[ns]AP[goproblems] (;B[os];W[pr] (;B[pq];W[or] (;B[ps];W[qs] (;B[rs] (;W[ls] (;B[ms];W[ps] (;B[ks];W[ss]) (;B[nr];W[ss])) (;B[ps];W[os] (;B[ms];W[qs]C[Do not play K4 unless you think you really need a ko threat]LB[jp:Threat] (;B[ks]C[Even if White plays T1 and K1 next, Black lives with double ko. If White takes one ko Black takes the other. White cannot connect either ko because Black would capture 4 or 6 stones and live. RIGHT]MA[ls]MA[ps]TR[qs]MA[ss]) (;B[jp];W[ks]C[If White ignores your threat the situation becomes an approach-move ko. White will have to ignore 2 more threats, nevertheless you could have lived without that.]) (;B[nr];W[ss]) (;B[ss];W[nr])) (;B[nr];W[qs];B[ks];W[js];B[ps]) (;B[qs];W[ms]) (;B[ks];W[js]C[This only helps White somewhat, but never mind.] (;B[ms];W[qs]C[Do not play K4 unless you think you really need a ko threat]LB[jp:Threat] (;B[ks]C[Even if White plays T1 next, Black lives with double ko. If White takes one ko Black takes the other. White cannot connect either ko because Black would capture 4 or 6 stones and live. RIGHT]) (;B[nr];W[ss]) (;B[jp];W[ks]C[If White ignores your threat the situation becomes an approach-move ko. White will have to ignore 2 more threats, nevertheless you could have lived without that.]) (;B[ss];W[nr])) (;B[nr];W[qs]C[Direct ko]) (;B[ss];W[ms]) (;B[qs];W[ms])) (;B[ss];W[ms])) (;B[nr];W[os] (;B[ps]C[Ko]) (;B[ms];W[ss]) (;B[ss];W[ms]) (;B[ks];W[js];B[ps])) (;B[os];W[nr] (;B[ms];W[ss]) (;B[ps];W[qs] (;B[ms];W[ss]) (;B[ps];W[ms]))) (;B[ks];W[ms] (;B[nr];W[ss]) (;B[ps];W[ss] (;B[nr];W[qs]) (;B[os];W[qs] (;B[ps];W[js]) (;B[os];W[nr]) (;B[js];W[is] (;B[ps];W[jr]) (;B[os];W[nr]) (;B[jr];W[jq]))) (;B[js];W[is] (;B[nr];W[qs]) (;B[os];W[qs] (;B[ps];W[jr]) (;B[os];W[nr]) (;B[jr];W[jq])) (;B[jr];W[jq]))) (;B[js];W[ss] (;B[ps];W[is] (;B[nr];W[qs]) (;B[os];W[qs]) (;B[jr];W[jq])) (;B[os];W[nr]) (;B[jr];W[nr]) (;B[is];W[nr])) (;B[os];W[ps])) (;B[ss];W[ms])) (;W[os] (;B[ms];W[ss] (;B[ks];W[js] (;B[ps]C[Double ko. White would have to win both to kill; if White connects Q1 then Black can capture a living shape.RIGHT]) (;B[nr];W[ls]) (;B[ls];W[nr])) (;B[nr];W[ls]) (;B[ls];W[ks]C[Direct ko]) (;B[js];W[ks]C[Approach-move ko.]) (;B[ps];W[jp]LB[jo:T]C[White plays a ko threat. Answer the threat at T if you feel you can. Otherwise, play otherwise.] (;B[jo];W[qs] (;B[ks]C[Correct! White can only get a double ko, so Black lives anyway.RIGHT]) (;B[nr];W[ls]) (;B[ls];W[ks]C[Direct ko.])) (;B[nr]C[Alive, but you could have answered the threat and still live. Effectively you lost a move.]) (;B[qs]C[You llive, but you could have answered the threat and still live. Effectively you lost a move.]) (;B[ks]C[Alive, but you could have answered the threat and still live. Effectively you lost a move.]) (;B[ls];W[qs]C[Approach move ko.]))) (;B[ps];W[ss] (;B[ks];W[ms] (;B[qs];W[js] (;B[ls];W[nr]) (;B[nr];W[ls])) (;B[nr];W[qs]C[Ko]) (;B[ls];W[qs]C[Approach-move ko])) (;B[nr];W[qs]C[Approach-move ko]) (;B[ls];W[ks]C[10000 year ko.]) (;B[ms];W[qs] (;B[ks]C[Double ko.RIGHT];W[js] (;B[ps]C[Double ko. White would have to win both to kill; if White connects Q1 then Black can capture a living shape.RIGHT]) (;B[nr];W[ls]) (;B[ls];W[nr])) (;B[nr];W[ls]) (;B[ls];W[ks]C[Direct ko])) (;B[qs];W[nr])))) (;B[nr]) (;B[os];W[rs]) (;B[ps];W[os] (;B[rs];W[ls] (;B[ms];W[ks]C[The situation becomes an approach-move ko. White will have to ignore 2 threats, nevertheless you could have lived without that.]) (;B[nr];W[ms]) (;B[ps];W[ms]) (;B[ks];W[ms])) (;B[ms];W[rs]) (;B[nr];W[rs] (;B[ms];W[ls]) (;B[ls];W[ks]) (;B[ks];W[ms])) (;B[ls];W[rs])) (;B[ms];W[rs]) (;B[ls];W[rs])) (;B[nr];W[ps] (;B[rs];W[ls] (;B[ms];W[os]) (;B[qs];W[os])) (;B[qs];W[os]) (;B[ls];W[rs];B[qs];W[os]) (;B[ms];W[os])) (;B[qs];W[ps] (;B[ms];W[os]) (;B[nr];W[os]) (;B[ls];W[ks];B[nr];W[os])) (;B[rs];W[ps] (;B[ls];W[nr] (;B[qs];W[ks]) (;B[ms];W[ks])) (;B[nr];W[ls] (;B[ms];W[os]) (;B[qs];W[os])) (;B[ms];W[ss];B[nr];W[os]) (;B[qs];W[ls] (;B[nr];W[os]) (;B[ms];W[ks]))) (;B[ms];W[ps] (;B[nr];W[os]) (;B[rs];W[ss];B[nr];W[os]) (;B[qs];W[os])) (;B[ls])) (;B[or];W[pq]) (;B[ps];W[pq]) (;B[nr];W[pq]) (;B[ms];W[pq]) (;B[rs];W[pq]) (;B[qs];W[pq]) (;B[ls];W[pq]) (;B[ks];W[pq])) (;B[or];W[pq] (;B[pr];W[rs] (;B[qs];W[os]) (;B[os];W[qs]) (;B[ls];W[qs])) (;B[os];W[pr]) (;B[rs];W[pr]) (;B[ls];W[pr])) (;B[pq];W[ls] (;B[os];W[or] (;B[ps];W[nr] (;B[ms];W[rs]) (;B[pr];W[rs]) (;B[rs];W[ms])) (;B[nr];W[ps] (;B[ms];W[os]) (;B[pr];W[os])) (;B[ms];W[ps] (;B[rs]C[Black is dead. If Black plays either of the marked points White connects at P1 and Black has just one eye. White can play the marked points and T1, L1 and R1 anytime.]MA[nr]MA[pr]) (;B[nr];W[os])) (;B[rs];W[ms] (;B[nr];W[ps]) (;B[ps];W[nr]) (;B[pr];W[ps]) (;B[ks];W[ps])) (;B[ks];W[js] (;B[ms];W[ps]) (;B[ps];W[nr] (;B[rs];W[ms]) (;B[ms];W[rs]) (;B[pr];W[rs])) (;B[nr];W[ps] (;B[ms];W[os]) (;B[pr];W[os])) (;B[rs];W[ms]))) (;B[ms];W[or] (;B[rs];W[ps]MA[nr]MA[pr]C[Black is dead. If Black plays either of the marked points White connects at P1 and Black has just one eye. White can play the marked points and T1, L1 and R1 anytime.]) (;B[ps];W[rs] (;B[os];W[nr]) (;B[nr];W[os]) (;B[pr];W[os])) (;B[ks];W[rs]) (;B[os];W[ps] (;B[rs]C[Black is dead. If Black plays either of the marked points White connects at P1 and Black has just one eye. White can play the marked points and T1, L1 and R1 anytime.]MA[nr]MA[pr]) (;B[nr]))) (;B[nr];W[ps] (;B[ms];W[os] (;B[rs];W[or]) (;B[or];W[rs])) (;B[or];W[ms]) (;B[pr];W[os]) (;B[os];W[or] (;B[ms];W[os]) (;B[pr];W[os]))) (;B[or];W[ms]) (;B[ps];W[ms] (;B[rs];W[or]) (;B[or];W[rs]) (;B[os];W[rs]) (;B[nr];W[rs]) (;B[ks];W[js] (;B[or];W[rs]) (;B[nr];W[rs]) (;B[os];W[rs]) (;B[rs];W[or]))) (;B[rs];W[ps] (;B[or];W[ms]) (;B[ms];W[or]C[Black is dead. If Black plays either of the marked points White connects at P1 and Black has just one eye. White can play the marked points and T1, L1 and R1 anytime.]MA[nr]MA[pr]) (;B[os];W[ms]) (;B[nr];W[os])) (;B[ks];W[ps] (;B[rs];W[ms]) (;B[or];W[ms]) (;B[ms];W[or] (;B[rs];W[pr]C[Black dies. White has one eye and Black none. If Black plays O2 then wP1 means Black can capture but still only has one eye.]) (;B[nr];W[os])) (;B[os];W[or] (;B[rs];W[ms]) (;B[ms];W[rs])))) (;B[pr];W[or] (;B[rs];W[ps] (;B[ls];W[pq]) (;B[nr];W[os] (;B[pq];W[ls]) (;B[ls];W[pq])) (;B[pq];W[ls] (;B[nr];W[os]) (;B[qs];W[os]) (;B[ms];W[os])) (;B[qs];W[os])) (;B[pq];W[ps] (;B[rs];W[ls] (;B[nr];W[os]) (;B[qs];W[os]) (;B[ms];W[os])) (;B[ls];W[rs]) (;B[qs];W[os]) (;B[nr];W[os] (;B[ls];W[rs]) (;B[rs];W[ls]))) (;B[ps];W[rs] (;B[os];W[nr]) (;B[nr];W[os]) (;B[ms];W[pq] (;B[nr];W[ls]) (;B[os];W[qs]))) (;B[nr];W[os] (;B[ps];W[rs]) (;B[rs];W[ps] (;B[pq];W[ls]) (;B[ls];W[pq])) (;B[pq];W[rs]) (;B[ls];W[pq] (;B[rs];W[ss]) (;B[ps];W[rs]))) (;B[os];W[ps] (;B[nr];W[os]) (;B[rs];W[pq]) (;B[pq];W[rs]) (;B[ls];W[pq];B[nr];W[os])) (;B[ls];W[pq] (;B[nr];W[os] (;B[rs];W[ss]) (;B[ps];W[rs])) (;B[os];W[ps];B[nr];W[os]) (;B[ps];W[rs] (;B[nr];W[os]) (;B[os];W[qs]) (;B[ms];W[ks])) (;B[rs];W[ps]))) (;B[nr];W[pq] (;B[pr];W[os] (;B[or];W[rs]) (;B[ps];W[rs]) (;B[rs];W[ps] (;B[or];W[ls]) (;B[ls];W[or])) (;B[ls];W[or] (;B[rs];W[ss]) (;B[ps];W[rs]))) (;B[os];W[pr]) (;B[or];W[pr]) (;B[ms];W[pr])) (;B[ms];W[pq] (;B[pr];W[or] (;B[ps];W[rs] (;B[nr];W[ls]) (;B[os];W[qs])) (;B[nr];W[ls]) (;B[rs];W[ps]) (;B[os];W[ps])) (;B[or];W[pr]) (;B[os];W[pr])) (;B[ls];W[pq] (;B[pr];W[or] (;B[nr];W[os]) (;B[os];W[ps]) (;B[ps];W[rs] (;B[nr];W[os]) (;B[os];W[qs]) (;B[ms];W[ks])) (;B[rs];W[ps])) (;B[or];W[pr]) (;B[os];W[pr])) (;B[ps];W[pq] (;B[pr];W[rs]) (;B[rs];W[pr]) (;B[or];W[pr]) (;B[nr];W[pr]) (;B[os];W[pr])) (;B[rs];W[or] (;B[pq];W[ls];B[ms];W[ps]MA[nr]MA[pr]C[Black is dead. If Black plays either of the marked points White connects at P1 and Black has just one eye. White can play the marked points and T1, L1 and R1 anytime.]) (;B[pr];W[ps] (;B[ls];W[pq]) (;B[nr];W[os] (;B[pq];W[ls]) (;B[ls];W[pq])) (;B[pq];W[ls] (;B[nr];W[os]) (;B[qs];W[os]) (;B[ms];W[os])) (;B[qs];W[os])) (;B[nr];W[ps] (;B[ls];W[pq];B[pr];W[os]) (;B[pq];W[ls] (;B[ms];W[os]) (;B[pr];W[os])) (;B[pr];W[os] (;B[pq];W[ls]) (;B[ls];W[pq]))) (;B[ps];W[pq] (;B[pr];W[ls] (;B[os];W[ms] (;B[nr];W[or]) (;B[ks];W[nr])) (;B[nr];W[ms]) (;B[ms];W[nr])) (;B[nr];W[pr]) (;B[os];W[pr])) (;B[ls];W[pq] (;B[pr];W[ps]) (;B[ps];W[pr]))) (;B[qs];W[pq] (;B[pr];W[os]) (;B[or];W[pr]) (;B[os];W[pr])))