Harry: Use magic to cheat on gambling, or do the arbitrage-y thing.

Lucius: Suddenly you don't understand anything.

I'd say Harry would trade with Lucius - Harry would testify under Veritaserum that Dumbledore confesed to Him, that he burned Narcissa. In exchange Lucius would let Hermione free.

Harry don't know if Dumbledore burned Narcissa, but probably can beat Veritaserum (according to Quirell), and with his evil side enabled he can risk trying it.

Similiar to "make Dumbledore turn himself in", but Dumbledore had chance to do that, and declined, and I don't know if Harry can blackmail Dumbledore serioulsy enough for this. But Harry don't need to blackmail Dumbledore.

PredictionBook registry - take one prediction a day to keep the hindsight bias away! - based on the speculation:

Harry's solution will be...

• nothing
• invoking Lucius's debt to whomever killed his supposed Imperiuser
• invoke the Imperius-debts of other Wizengamot members
• make Dumbledore turn himself in to Lucius in exchange for Hermione's freedom
• threaten to destroy Azkaban
• reveal the truth about Bellatrix's escape
• offer the Wizengamot Voldemort's true identity (Quirrel)
• accept Hermione's imprisonment but order the Dementors to leave her alone
• destroying one of the Dementors

• using the Time-turner

  • to alter Hermione's testimony to something easily falsifiable
  • to affect Lucius in some way
  • to smuggle Hermione out under the Cloak
• ask for a trial by combat
• have Quirrel make Bella confess to the crime
• confess to the attack
• demonstrate Hermione's wand did not cast the curse with Priori Incantatem

(These are not all mutually exclusive, and I didn't set down and make them all sum to 100%.)

The author's clues are pushing in two different directions. "Taboo tradeoffs" in the title, and that Harry's Dark side is delivering the solution, implies an answer that is morally unnerving or at least cold-blooded.

The author's line about Harry shifting from seeing the Wizengamot voters as "wallpaper" to seeing individuals with agency, "PCs", and the line about remembering the laws of magical Britain, implies an answer that involves the incentives and 'rules of the game' of the other Wizengamot members besides Lucius and Dumbledore.

None of the solutions I've seen (let alone the few I've thought of) seem both Dark/taboo and social/voters-are-PCs.

Harry calling in the (nominally) Imperiused voters' debts: clever, invokes customs of magical Britain, makes the voters PCs rather than wallpaper, but not very Dark or taboo.

Harry threatens the crowd with the Dementor somehow, or browbeats Dumbledore into ruining his reputation: Dark/taboo, but doesn't invoke the customs of magical Britain or treat the other Wizengamot voters as PCs.

Is there a solution that both invokes magical Britain's laws / makes PCs of the voters and involves some alarmingly Dark/taboo move or trade by Harry?

Boy-Who-Lived marries Draco Malfoy?

That's a reasonable narrative. We'll have to wait to see exactly how it played out, of course, but I wouldn't find that version surprising at all.

Conversely, however, remember how many of the basic protections we take for granted that don't exist in the wizarding world. In a lot of ways it's a medieval society, and very few leaders from that era would have flinched at doing something utterly brutal to make a point. Even real-world terrorist groups try to pretend to play by the rules of civilized society, because those rules are so expected that ignoring them would damage their cause terribly. It's the same as dictators running "free elections" - they're not, but they pretend for the PR value. I doubt that PR value exists in the wizarding world.

How would Harry even get to the trial in the first place? Dumbledore won't let him leave Hogwarts, and if he did, why should the Wizengamot admit him to the proceedings unless e.g. Dumbledore requested it? And why would D. do that unless he expected Harry to succeed in helping Hermione escape? But if D. wanted Hermione to escape illegally (possible but unlikely IMO), he could surely arrange that himself without Harry's help and presence. (Maybe he'd borrow the cloak...)

If Harry does not manage to find the real culprit, then how does he save Hermione from having her wand broken?

Breakout/Direct Attack on the Wizengamot / Malfoy Manor

• Transfigure a one-atom line of antimatter through the earth's crust all the way to the Wizengamot or Malfoy Manor, and then a small bubble there. His wand is then touching the item to be transformed, and it will work.

• Go to Azkaban and round up a few hundred dementors.

Stealth

• Transferring the cloak of invisibility to her somehow.

Bringing Hermione under the aegis of a noble house

• Adoption or marriage

Did anybody bothered to check previous spells on Hermione, Snape, and Quirrell wands? EDIT: Ok, we''re told Quirrell cast tens of spells since 06:33, still - they should check just to be sure.

Now it seems Harry should just kidnapp Hermione and hide here somewhere(And give her cloak to hide her from tracking spels).

"Professor Quirrell had cast tracking Charms because he had learned of a person with a motive to harm Mr. Malfoy. Professor Quirrell had refused to identify this person." hmm, why hadn't they used veritaserum on Quirrell to ask him who had the motive? Seems like usefull thing to know after murder attempt..

Also - Quirrell said he found out about Draco at 06:33 - just half an hour too late to use Time Turner and check what happened or to stop Hermione in the first place. Funny coincidence.

Hat and Cloak told Hermione "you are a Muggleborn and yet you possess a power of wizardry greater than any pureblood."

Lucius can't believe that. He can't even afford for that belief to exist, so I don't see him uttering it, even as flattery he "knows" to be false.

From chapter 14

"Turning into a cat doesn't even BEGIN to compare to this. You know right up until this moment I had this awful suppressed thought somewhere in the back of my mind that the only remaining answer was that my whole universe was a computer simulation like in the book Simulacron 3 but now even that is ruled out because this little toy ISN'T TURING COMPUTABLE! A Turing machine could simulate going back into a defined moment of the past and computing a different future from there, an oracle machine could rely on the halting behavior of lower-order machines, but what you're saying is that reality somehow self-consistently computes in one sweep using information that hasn't... happened... yet..."