This problem shows a tesuji you can often use in real games, too...
Please find the best result for Black!
(japanese rules)
(;GM[1]FF[4]CA[UTF-8]AP[CGoban:2]ST[2]
RU[Japanese]SZ[4]KM[0.00]
PW[Weiß]PB[Schwarz]AW[ba][bb][ac]AB[cb][db][dd]C[Black to move - what's the best he can do?]
(;B[bc]CR[bc]
(;W[cc]CR[cc]
;B[bd]CR[bd]
(;W[ca]CR[ca]
;B[ab]CR[ab]C[Black has an eye, White has no eye, so... Black wins! RIGHT CHOICE])
(;W[ab]CR[ab]
(;B[ca]CR[ca]C[White is short of liberties and can't atari with A1, so Black wins. RIGHT CHOICE])
(;B[cd]CR[cd]
;W[ca]CR[ca]C[Seki, Black wins by one point (the prisoner). This is not as good as the solution!])
(;B[dc]CR[dc]
;W[ca]CR[ca]C[Seki, Black wins by one point (the prisoner). This is not as good as the solution!])))
(;W[bd]CR[bd]
;B[cc]CR[cc]
(;W[ca]CR[ca]
(;B[ab]CR[ab]C['One eye beats no eye' - Black wins!])
(;B[da]CR[da]
;W[ab]CR[ab]C[Seki & jigo!]))
(;W[ab]CR[ab]
;B[ca]CR[ca]C[Black wins!])))
(;B[cc]CR[cc]
;W[bc]CR[bc]
(;B[ca]CR[ca]
;W[bd]CR[bd]
;B[cd]CR[cd]C[White wins by one point.])
(;B[bd]CR[bd]
;W[ca]CR[ca]
(;B[ab]CR[ab]
;W[aa]CR[aa]C[Seki, White wins by one point (the prisoner).])
(;B[aa]CR[aa]
;W[ab]CR[ab]C[Seki, White wins by one point (the prisoner).])))
(;B[bd]CR[bd]
;W[bc]CR[bc]
;B[cc]CR[cc]
;W[ca]CR[ca]
(;B[ab]CR[ab]
;W[aa]CR[aa]C[Seki, White wins by one point (the prisoner).])
(;B[aa]CR[aa]
;W[ab]CR[ab]C[Seki, White wins by one point (the prisoner).]))
(;B[ca]CR[ca]
;W[cc]CR[cc]C[White wins!]))
