Problem	13431
Created	2010-02-10
Source	Problem 13428 by thornhead
Rating

Difficulty	6 dan
Average Solve Time	78 secs
User Attempts	99 / 332
Solve Ratio Rating	4 kyu
	rating history

Thornhead's solution was incorrect and his problem was deactivated, probably due to my claim that it had no possible solution path at all. Well, I could not be more wrong. So here goes, with apologies to Thornhead and thanks to all whose comments helped sharpen up this problem.

(;AB[ro]AB[qo]AB[qp]AB[pp]AB[oq]AB[or]AB[rq]AW[op]AW[np]AW[nq]AW[nr]AW[sq]AW[sn]AW[rn]AW[qn]AW[po]AW[pn]C[Black to find unconditional life.]AW[qr]AP[goproblems] (;B[sr];W[ps] (;B[rr];W[sp] (;B[so]) (;B[qs];W[rs];B[so];W[os]) (;B[rs];W[so] (;B[pq];W[os]) (;B[os];W[pq])) (;B[pq];W[os] (;B[so];W[rs]) (;B[rs];W[so]) (;B[pr];W[rs])) (;B[pr];W[os]) (;B[qq];W[rs];B[os];W[ns] (;B[pq];W[so]) (;B[ss];W[pq]) (;B[so];W[pq])) (;B[os];W[pq] (;B[so];W[rs]) (;B[rs];W[so]))) (;B[os];W[pq] (;B[rr] (;W[rs]) (;W[sp] (;B[so];W[rs]) (;B[rs];W[so]))) (;B[sp];W[rr])) (;B[pq];W[os] (;B[rr];W[sp] (;B[so];W[rs]) (;B[rs];W[so]) (;B[pr];W[rs])) (;B[sp];W[rr])) (;B[sp];W[rr] (;B[os];W[pq]) (;B[qq];W[os]) (;B[pq];W[os]) (;B[pr];W[os]))) (;B[sp];W[rr] (;B[sr];W[pr]) (;B[pq];W[ps];B[os];W[sr] (;B[pr] (;W[qs]) (;W[so] (;B[qs];W[qq] (;B[rp];W[ns]) (;B[rs];W[rp]) (;B[ss];W[rp])) (;B[qq];W[rs]C[Double ko, Black dies];B[qs];W[rp]C[Double ko, Black dies]) (;B[rs];W[qq];B[rp];W[ns]) (;B[rp];W[qs]))) (;B[qq];W[rs] (;B[pr];W[so]C[Double ko, Black dies];B[qs];W[rp]C[Double ko, Black dies]) (;B[so];W[ns])) (;B[so];W[pr];B[rs];W[ns]) (;B[rs];W[so];B[pr];W[qq];B[rp];W[ns]))) (;B[pq];W[sp];B[so];W[rr];B[rp];W[sr];B[pr];W[ps];B[os];W[qs]C[CHOICE]) (;B[rr];W[ps]C[CHOICE] (;B[sp];W[rs] (;B[sr];W[pq]MA[qq]MA[so]C[RIGHT]) (;B[pq];W[os] (;B[sr]C[RIGHT]) (;B[qq];W[sr] (;B[ss];W[sr]) (;B[pr];W[qs];B[ss];W[sr])) (;B[pr];W[sr] (;B[ss];W[sr]) (;B[qq];W[qs];B[ss];W[sr])) (;B[so];W[sr] (;B[ss];W[sr]) (;B[qq];W[qs];B[ss];W[sr])) (;B[ss];W[sr];B[ss];W[sr])) (;B[qq];W[os] (;B[sr]C[RIGHT]) (;B[pq];W[sr] (;B[ss];W[sr]) (;B[pr];W[qs];B[ss];W[sr])) (;B[pr];W[sr] (;B[ss];W[sr] (;B[qs]C[Just ko]) (;B[sq];W[pq]) (;B[pq];W[qs])) (;B[qs]C[Just ko]) (;B[pq];W[qs];B[ss];W[sr])) (;B[so];W[sr])) (;B[os];W[pq] (;B[qq];W[ns] (;B[sr]C[RIGHT]) (;B[pr];W[pq] (;B[sr]C[RIGHT]) (;B[so];W[sr])) (;B[so];W[sr])) (;B[sr]C[RIGHT]) (;B[so];W[sr] (;B[qq];W[rp]) (;B[ss];W[sr] (;B[qq];W[ns] (;B[pr];W[pq]) (;B[sq];W[rp])) (;B[sq];W[ns] (;B[ss];W[qs]) (;B[qq];W[rp]))))) (;B[pr];W[os] (;B[sr]C[RIGHT]) (;B[so];W[sr] (;B[ss];W[sr]) (;B[qq];W[pq])) (;B[pq];W[sr] (;B[ss];W[sr]) (;B[qq]))) (;B[so];W[sr];B[os];W[pq] (;B[qq];W[rp]) (;B[ss];W[sr] (;B[qq];W[ns] (;B[pr];W[pq]) (;B[sq];W[rp])) (;B[sq];W[ns] (;B[ss];W[qs]) (;B[qq]))))) (;B[rs];W[so] (;B[sr];W[sp] (;B[pq];W[os]) (;B[os];W[pq])) (;B[os];W[pq] (;B[sr];W[sp]) (;B[sp];W[qq] (;B[rp];W[sr]) (;B[sr];W[rp]) (;B[qs];W[rp])) (;B[qq];W[ns];B[sp];W[rp]C[Ko])) (;B[pq];W[sp]) (;B[pr];W[os];B[sp];W[rp]C[Ko]) (;B[sp];W[rp]C[Ko])) (;B[pq];W[so] (;B[sp];W[rp]C[Ko]) (;B[sr];W[sp] (;B[os] (;W[rs]) (;W[rp] (;B[pr];W[rs]C[Ko]) (;B[qq];W[rs]) (;B[rs];W[qq]))) (;B[rp];W[os]) (;B[pr];W[os]) (;B[rs];W[os])) (;B[os];W[sr] (;B[sp];W[rp]C[Ko]) (;B[pr];W[qs] (;B[sp];W[rp]C[Ko]) (;B[rp];W[sp]) (;B[ss];W[sp]) (;B[rs];W[sp]) (;B[qq];W[sp])) (;B[qq];W[sp]) (;B[rp];W[sp]) (;B[rs];W[sp]) (;B[qs];W[rs] (;B[pr];W[qs] (;B[sp];W[rp]C[Ko]) (;B[qq];W[sp]) (;B[rp];W[sp])) (;B[rp];W[sp]) (;B[sp];W[rp]C[Ko]) (;B[qq];W[sp])) (;B[ss];W[sp])) (;B[rp];W[sp]) (;B[rs];W[sp]) (;B[pr];W[sp])) (;B[os];W[pq] (;B[sr] (;W[rs]) (;W[sp])) (;B[sp];W[qq] (;B[rs];W[so] (;B[rp];W[sr]) (;B[sr];W[rp]) (;B[qs];W[rp])) (;B[sr];W[so] (;B[rp];W[rs]) (;B[rs];W[rp])) (;B[so];W[rp]) (;B[rp];W[rs])) (;B[qq];W[ns];B[sp];W[rs];B[sr]C[RIGHT]) (;B[rs];W[so] (;B[sr];W[sp]) (;B[sp];W[qq] (;B[rp];W[sr]) (;B[sr];W[rp]) (;B[qs];W[rp])) (;B[qq];W[ns];B[sp];W[rp]C[Ko]))) (;B[pr];W[os] (;B[rs];W[so];B[sp];W[rp]C[Ko]) (;B[sp] (;W[so] (;B[sr];W[qq] (;B[rp];W[rs]) (;B[rs];W[pq];B[rp]C[RIGHT]) (;B[pq];W[rp]) (;B[qs];W[rs])) (;B[rp];W[rs]) (;B[qq];W[pq];B[sr]C[RIGHT]) (;B[pq];W[rp]C[Ko]) (;B[rs];W[rp]C[Ko])) (;W[rs] (;B[sr]C[RIGHT]) (;B[so];W[sr] (;B[ss];W[sr]) (;B[qq];W[pq])) (;B[pq];W[sr]))) (;B[so];W[rs] (;B[sp];W[sr] (;B[ss];W[sr]) (;B[qq];W[pq])) (;B[sr];W[sp])) (;B[sr];W[sp]) (;B[pq];W[rs]) (;B[qq];W[rs] (;B[sr];W[sp] (;B[so];W[pq]) (;B[qs]C[Ko]) (;B[ss];W[pq]) (;B[pq];W[qs])) (;B[sp];W[sr] (;B[ss];W[sr] (;B[qs]C[Just ko]) (;B[sq];W[pq]) (;B[pq];W[qs])) (;B[qs]C[Just ko]) (;B[pq])) (;B[qs]C[Ko]))) (;B[sr];W[sp] (;B[so]) (;B[qs];W[rs];B[so];W[os]) (;B[rs];W[so] (;B[pq];W[os]) (;B[os];W[pq])) (;B[pq];W[os] (;B[so];W[rs]) (;B[rs];W[so]) (;B[pr];W[rs])) (;B[pr];W[os]) (;B[qq];W[rs];B[os];W[ns] (;B[pq];W[so]) (;B[ss];W[pq]) (;B[so];W[pq])) (;B[os];W[pq] (;B[so];W[rs]) (;B[rs];W[so]))) (;B[rp];W[rs];B[os];W[pq]) (;B[so];W[rs] (;B[sr];W[sp];B[os];W[pq]) (;B[os];W[pq];B[sp];W[sr] (;B[qq];W[rp]) (;B[ss];W[sr] (;B[qq];W[ns] (;B[pr];W[pq]) (;B[sq];W[rp])) (;B[sq];W[ns] (;B[ss];W[qs]) (;B[qq]))))) (;B[qq];W[rs] (;B[pr];W[os] (;B[sr];W[sp] (;B[so];W[pq]) (;B[qs]C[Ko]) (;B[ss];W[pq]) (;B[pq];W[qs])) (;B[sp]) (;B[qs]C[Ko])) (;B[sp];W[os] (;B[sr]C[RIGHT]) (;B[pq]) (;B[pr];W[sr] (;B[ss];W[sr] (;B[qs]C[Just ko]) (;B[sq];W[pq]) (;B[pq];W[qs])) (;B[qs]C[Just ko]) (;B[pq])) (;B[so];W[sr])) (;B[sr];W[sp];B[os];W[ns] (;B[pq];W[so]) (;B[ss];W[pq]) (;B[so];W[pq])) (;B[os] (;W[ns] (;B[sp];W[pq];B[sr]C[RIGHT]) (;B[pq];W[so] (;B[pr];W[qs] (;B[sr];W[sp]) (;B[sp];W[rp]C[Ko]) (;B[ss];W[qs];B[sp];W[rp]C[Ko])) (;B[sr];W[sp]) (;B[sp];W[rp]C[Ko])) (;B[sr];W[sp] (;B[pq];W[so]) (;B[ss];W[pq]) (;B[so];W[pq]))) (;W[sp];B[pr])))) (;B[ps];W[rr] (;B[sp];W[sr] (;B[so];W[pq]) (;B[pq];W[so] (;B[rp];W[pr]) (;B[qs];W[qq];B[rp];W[rs])) (;B[qq];W[so]C[Ko])) (;B[so];W[pq] (;B[qq];W[pr]) (;B[pr];W[qq])) (;B[qq];W[sp];B[so];W[pr] (;B[pq];W[qs] (;B[ns];W[ms]) (;B[os];W[ns])) (;B[sr];W[ss] (;B[pq];W[qs]) (;B[qs];W[pq]) (;B[os];W[pq]))) (;B[pr];W[sp];B[so];W[qq] (;B[pq];W[rp]) (;B[rp];W[pq])) (;B[pq];W[sp];B[so];W[qs]) (;B[qs];W[sp];B[so];W[pq] (;B[pr];W[qq]) (;B[qq];W[rp]) (;B[rp];W[qq]) (;B[sr];W[ss]) (;B[rs];W[pr])) (;B[rp];W[pq])) (;B[so];W[rr] (;B[sp];W[pq]) (;B[pq];W[sp];B[rp];W[sr];B[pr];W[ps];B[os];W[qs]C[CHOICE]) (;B[pr];W[qq] (;B[rp];W[pq]) (;B[sp];W[pq];B[sr];W[ps]) (;B[pq];W[rp] (;B[sp];W[rq]) (;B[qs];W[sp]))) (;B[qq];W[pr]) (;B[os];W[pq]) (;B[ps];W[pq] (;B[qq];W[pr]) (;B[pr];W[qq]))) (;B[pr];W[rr] (;B[sp];W[sr] (;B[so];W[qq] (;B[pq];W[ps] (;B[os];W[rs];B[qs];W[rp]C[Black dies with double ko]) (;B[qs];W[rs];B[os]C[Black dies with double ko])) (;B[qs];W[pq])) (;B[qq];W[so]C[Ko]) (;B[pq];W[so] (;B[qs];W[qq] (;B[rp];W[os]) (;B[rs];W[rp])) (;B[qq];W[ps] (;B[os];W[rs];B[qs];W[rp]C[Double ko, Black dies]) (;B[qs];W[rs];B[os]C[Black dies with double ko])) (;B[rp];W[qs])) (;B[qs];W[qq] (;B[pq];W[so] (;B[rp];W[os]) (;B[rs];W[rp])) (;B[so];W[pq]) (;B[rs];W[so])) (;B[rp];W[pq];B[qq];W[so])) (;B[qq];W[sp] (;B[so];W[sr] (;B[qs];W[rp] (;B[pq];W[os]) (;B[rs];W[pq])) (;B[pq];W[qs])) (;B[sr];W[ss];B[so];W[qs]) (;B[qs];W[so])) (;B[so];W[qq] (;B[rp];W[pq]) (;B[sp];W[pq];B[sr];W[ps]) (;B[pq];W[rp] (;B[sp];W[rq]) (;B[qs];W[sp]))) (;B[sr];W[sp] (;B[so];W[ss] (;B[rp];W[pq] (;B[sr];W[ps] (;B[qq];W[os]) (;B[rs];W[os]) (;B[qs];W[os]) (;B[os];W[ns])) (;B[qq];W[pq])) (;B[qq];W[qs]) (;B[qs];W[qq])) (;B[qq];W[ss];B[so];W[qs]) (;B[ss];W[so]) (;B[rp];W[so]) (;B[qs];W[so]))) (;B[os];W[rr] (;B[sp];W[pq]) (;B[pq];W[sp] (;B[so]) (;B[sr];W[ss] (;B[so];W[qs]) (;B[qs];W[so]))) (;B[pr];W[qq];B[sp];W[pq];B[sr];W[ns]) (;B[so];W[pq]) (;B[qq];W[pr] (;B[pq];W[sp] (;B[so];W[sr]) (;B[sr];W[ss];B[so];W[ps])) (;B[sp];W[pq]))) (;B[qs];W[rr] (;B[pr];W[sp] (;B[so];W[qq] (;B[rp];W[pq]) (;B[pq];W[rp]) (;B[sr];W[ss]) (;B[rs];W[rp])) (;B[sr];W[ss] (;B[so];W[qq]) (;B[rp];W[so]) (;B[qq];W[so])) (;B[qq];W[so]) (;B[rs];W[sr];B[so];W[qq] (;B[pq];W[rp]) (;B[rp];W[pq]))) (;B[pq];W[sp] (;B[so] (;W[sr] (;B[qq];W[rs]) (;B[rs];W[qq]) (;B[pr];W[rs])) (;W[ps];B[pr])) (;B[sr];W[so] (;B[rs];W[ps]) (;B[ps];W[ss]))) (;B[sp];W[pr] (;B[pq];W[os]) (;B[ps];W[pq]) (;B[os];W[pq] (;B[sr];W[ns]) (;B[ps];W[ns]) (;B[rs];W[ns])) (;B[sr];W[pq]) (;B[qq];W[pq]))) (;B[rs];W[rr] (;B[sp];W[sr] (;B[pr];W[qq] (;B[qs];W[so]) (;B[so];W[pq])) (;B[qq];W[pr]) (;B[pq];W[qq] (;B[rp];W[qs]) (;B[pr];W[so] (;B[rp];W[os]) (;B[qs];W[rp])) (;B[qs];W[so] (;B[rp];W[os]) (;B[pr];W[rp]))) (;B[so];W[pq])) (;B[qq];W[pr] (;B[ps];W[pq]) (;B[pq];W[os]) (;B[os];W[pq]) (;B[sp];W[pq])) (;B[pr];W[qq];B[sp];W[sr] (;B[qs]) (;B[so];W[pq])) (;B[pq];W[sp] (;B[sr];W[so] (;B[qs];W[ps]) (;B[pr];W[qs]) (;B[qq];W[qs])) (;B[so];W[sr];B[ps];W[qs]))) (;B[qq];W[rr] (;B[sp];W[pr]) (;B[pr];W[sp] (;B[so];W[sr] (;B[qs];W[rp] (;B[pq];W[os]) (;B[rs];W[pq])) (;B[pq];W[qs])) (;B[sr];W[ss];B[so];W[qs]) (;B[qs];W[so])) (;B[sr];W[pr]) (;B[os];W[pr] (;B[pq];W[sp] (;B[so];W[sr]) (;B[sr];W[ss];B[so];W[ps])) (;B[sp];W[pq])) (;B[ps];W[sp];B[so];W[pr] (;B[pq];W[qs] (;B[ns];W[ms]) (;B[os];W[ns])) (;B[sr];W[ss] (;B[pq];W[qs]) (;B[qs];W[pq]) (;B[os];W[pq])))))