(;AB[ab]AB[bb]AB[bc]AB[cc]AB[dd]AB[de]AB[cf]AB[be]AB[ae]AW[bf]AW[bg]AW[cg]AW[dg]AW[ef]AW[ee]AW[ed]AW[dc]AW[db]AW[cb]AW[ba]C[Kill black. This problem is a little subtle.]AP[goproblems]
(;W[ce];B[cd]
(;W[df];B[ad]C[Black has two eyes. He lives.])
(;W[ad];B[df]C[Black has two eyes. He lives.]
(;W[af];B[bd]C[Black has two eyes. He lives.])
(;W[bd];B[ac]C[Black has two eyes. He lives.])
(;W[ac];B[bd]C[Black has two eyes. He lives.])
(;W[aa];B[ca]C[Black thanks you for the extra stones!])
(;W[ca];B[bd]C[Black has two eyes. He lives.]))
(;W[ac];B[ad]C[Black thanks you for the donation.])
(;W[bd];B[ad]C[Black thanks you for the donation.])
(;W[aa];B[ca]C[Black thanks you for the donation.])
(;W[ca];B[ad]C[Black makes two eyes. He lives.])
(;W[af];B[ad]C[Black makes two eyes. He lives.]))
(;W[ad]
(;B[bd]C[CHOICE]
(;W[ce]C[You found the answer! Black cannot make two eyes.RIGHT])
(;W[df];B[ce]C[Black made two eyes. He lives.])
(;W[cd];B[ce]C[Black thanks you for your sacrifice.])
(;W[af];B[ce]C[Black has two eyes. He lives.])
(;W[aa];B[ca]C[You're just being silly!])
(;W[ca];B[ce]C[Black has two eyes, and lives.]))
(;B[df]C[CHOICE]
(;W[cd];B[ce]
(;W[bd]C[Black is left with a straight three. Even if he captures at A17, youcan kill him. Good job!RIGHT])
(;W[aa];B[bd]C[So close!])
(;W[ca];B[bd]C[So close!])
(;W[af];B[bd]C[So close!])
(;W[ac];B[bd]C[You're just being silly...]))
(;W[bd];B[cd]
(;W[af];B[ac]C[At this point, black has two eyes. He lives.]
(;W[ad];B[bd]C[Black clearly has two eyes. He lives.])
(;W[bd];B[ad]C[Black clearly has two eyes. He lives.])
(;W[aa];B[ad]C[Black clearly has two eyes. He lives.])
(;W[ec];B[ad]C[Black clearly has two eyes. He lives.])
(;W[ca];B[ad]C[Black clearly has two eyes. He lives.]))
(;W[ag];B[ac]C[Black has two eyes. He lives.])
(;W[aa];B[ca]C[You've found the secret message!])
(;W[ca];B[ac]C[Black has two eyes. He lives.]))
(;W[ce];B[cd]
(;W[af];B[bd]C[Black has two eyes. He lives.])
(;W[bd];B[ac]C[Black has two eyes. He lives.])
(;W[ac];B[bd]C[Black has two eyes. He lives.])
(;W[aa];B[ca]C[Black thanks you for the extra stones!])
(;W[ca];B[bd]C[Black has two eyes. He lives.]))
(;W[ac];B[bd]C[Black has two eyes. He lives.])
(;W[af];B[bd]C[Black has two eyes. Good binocular vision.])
(;W[aa];B[ca]C[Black thanks you for your sacrifice.])
(;W[ca];B[cd]C[Black has two eyes.])))
(;W[bd];B[cd]
(;W[df];B[ad]C[Black has two eyes, and lives.])
(;W[ad];B[df]C[]
(;W[af];B[ac]
(;W[ad];B[bd]C[Black clearly has two eyes. He lives.])
(;W[bd];B[ad]C[Black clearly has two eyes. He lives.])
(;W[aa];B[ad]C[Black clearly has two eyes. He lives.])
(;W[ec];B[ad]C[Black clearly has two eyes. He lives.])
(;W[ca];B[ad]C[Black clearly has two eyes. He lives.]))
(;W[aa];B[ca]C[You don't need to sacrifice stones to solve this problem.])
(;W[ca];B[ac]C[Black has two eyes. He lives.])
(;W[ag];B[ac]C[Black has two eyes. He lives.])
(;W[ec];B[ac]C[Black has two eyes. He lives.]))
(;W[ac];B[ad]C[Black thanks you for the two eyes.])
(;W[af];B[df]C[Black has two eyes, and lives.])
(;W[aa];B[ca]C[Thank you for the sacrifice!])
(;W[ca];B[df]C[Black lives with two eyes.]))
(;W[cd];B[bd]C[You can't stop black from moving in C15 next move, and making a second eye.])
(;W[ac];B[ad]C[Black now has two eyes.])
(;W[df];B[ad]
(;W[ce];B[cd]C[Black lives with two eyes. At least, you got one stone...])
(;W[cd];B[ce]C[Black lives with two eyes.])
(;W[bd];B[ce]C[Black lives with two eyes.])
(;W[af];B[ce]C[Black lives with two eyes.])
(;W[aa];B[ca]C[Black thanks you for your sacrifice.])
(;W[ca];B[ce]C[Black lives with two eyes.]))
(;W[aa];B[ca]C[No, you don't need to sacrifice stones to win this problem!])
(;W[ca];B[ad]
(;W[ce];B[cd])
(;W[df];B[ce]C[Black has two eyes. He lives.])
(;W[af];B[df]C[C15 and C16 remain as ko threats, nothing more. Black has two eyes.])
(;W[cd];B[ce]C[Black has two eyes. He lives.])
(;W[bd];B[df]C[C15 and C16 remain as ko threats, nothing more. Black has two eyes.])
(;W[aa];B[df]C[C15 and C16 remain as ko threats, nothing more. Black has two eyes.]))
(;W[af];B[ad]
(;W[df];B[ce]C[Black has two eyes. He lives.])
(;W[ce];B[cd]C[Black has two and a half eyes. That's more than enough to live.])
(;W[cd];B[ce]C[Black has two eyes. He lives.])
(;W[bd];B[cd]C[Black has two eyes. That's enough to live.])
(;W[aa];B[ca]C[Thank you for the sacrifice!])))