Go (Baduk, Weiqi) problems with solutions

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Life-and-death problem (tsumego) 046

Black to play. How can they live?

(;
GM[1]FF[4]VW[]AP[goproblems.ru]
SZ[19]
ST[1]
AB[br][cr][cq][cp][dp][ep][fp][gp][do][dn][dm][gn][gm]
AW[bq][bp][co][cn][cm][ck][dl][el][fl][gl][hm][hn][ho][hp][hq][gq][fr][dr][dq][fn][eo]
C[Black to play
How can they live?
];B[aq]
TE[1]C[Correct answer
];W[bo]
(;B[cs]
C[White must answer Black 3 at the bottom.
]
(;W[ds];B[fm];W[em];B[en];W[go];B[fo])
(;W[go]
C[If they take away Black’s eye in the centre…
];B[er];W[eq];B[fq];W[es];B[ds]
C[Black captures the stones with a well-known technique.
]))
(;B[fm]
BM[1]C[Wrong continuation
Black should not hurry with 3.
];W[em];B[en];W[go];B[fo];W[cs];B[bs];W[ar];B[er]
;W[eq];B[fq];W[es];B[ds]
C[A ko fight arises.
]))

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