Its the only solution I've seen that proves Hermoine innocence AND gains Harry an advantage. I think it was foreshadowed back in Self Actualization.

With a plan this complex there are many variables, so I just filled in my favorite guesses such as the person being framed, the order, etc.

Harry realizes the plan in that moment of desperation then gets the vote stopped to admit new evidence. He then presents to the court the testimony of George and Fred Weasley who say that during the night of the attempted murder they were out of their bed pulling a prank, when they saw Lord Jugson entering the Trophy room. They thought it was strange but since they were out of bed pulling a prank they didn’t want to tell anyone, until they realized that morning it could be connected. They then went straight to a Professor who brought them to the Wizengamot, and they repeat their testimony under veritaserum.

Lord Jugson claims they were false memory charmed, but Harry responds to this by saying that if you are so confident of it why not let us examine the last spells cast on your wand, and that of Hermoine’s and Draco’s? After all you have nothing to hide. Lord Jugson agrees and hands over his wand, and then priori incantum reveals to his shock that his wand has been used recently to do the imperius, obliviate and the false memory charm. Hermoine's wand has been faked to use the Blood Chilling charm but Draco's has no evidence of a duel past the army fight on it at all.

Harry explains that Lord Jugson in a fit of rage at Draco for losing to a mudblood and Hermoine for beating him made a plot to punish them both after the army fight. He disappeared after the fight, and remained in Hogwarts to imperius Draco to challenge Hermoine to a duel at midnight. Then he either simply stayed in Hogwarts until midnight, used a secret passage or apparated outside the wards and flew in a broomstick, or used the floo network to enter Hogwarts right before midnight. He made his way to the trophy room, stunned Draco and Hermoine as they entered, disillusioned them all, and took them outside of the wards of Hogwarts to do the obliviation and false memory charms returning them after the deed was done. Lord Jugson won’t have an alibi for the hours of 11:30 to 12:30 as everyone in his household would be asleep at the time.

He used Hermoine's wand to cast spells simulating a duel followed by the blood chilling charm figuring that when Draco died he could prompt an investigation into her which would reveal the evidence on her wand combined with veritaserum to convict her. He obliviated Draco and false memory charmed him as well just in case Draco was discovered, but he didn't bother to tamper with Draco's wand figuring no one would have a reason to investigate it, and the wands show this.

Harry further explains that Lord Jugson decided that Draco had become too friendly to mudbloods and was no longer fit to be a leader of the blood purists. By killing him after his public showdown with Hermoine he could get rid of Draco, Hermoine AND set his own son up to assume leadership of the blood purists now that the Malfoy’s had no heir. After the plot ended he obliviated himself (if he isn't an occlumens) to safely hide the plot forever. Lord Jugson is sentenced to Azkhaban, by Harry invoking Lord Malfoy's blood debt to Harry to decide the sentencing, Hermoine is freed and the blood purists lose face politically for wanting to kill an innocent girl.

In my next post I will explain how Harry did it.

Let me set the stage first. For a bare minimum solution Hermoine has to be proven innocent so she can return to school without someone trying to kill her to score points for Malfoy. For an optimal solution Harry teaches his enemies that poking him with a stick is very dangerous, and manages to turn this to his advantage by harming an enemy. But in no way is any solution good enough if it doesn’t end up with Hermoine proven innocent to the world.

He has a time-turner, an invisibility cloak, possibly the blood debts of everyone who claimed to be imperiused, possibly the wands as evidence, a very analytical mind that is currently very open to ‘dark’ ideas, and multiple people of different skills/motivations that he can coerce or get to help him.

Lord Jugson is someone that really doesn’t seem to have much a point in the story so far. It makes the most sense to me as someone who is being built up just to be the scapegoat. “"It would be justice for his past crimes, and I'd only do it if Jugson made the first move. The point isn't to make people scared of me as a wild card, after all. It's to teach them that neutrals are perfectly safe from me, and poking me with a stick is incredibly dangerous."” Also, The boy smiled, now with a touch of coldness again. "Okay, I'll figure out some way to set it up so that it looks like Lord Jugson betrayed his own side."

A big gaping hole like introducing the wands for evidence is far too obvious for Harry to pretend it doesn’t exist anymore, so that is avenue worth approaching. However Cloak and Hat is far too clever to have forgotten to doctor the wands, unless he deliberately wanted the wands to prove.
It would also be just like Harry to use the enemies tactics against them, and so the idea of thwarting an evil plot based on false memory charms by using false memory charms to thwart it would be appealing.

They could use some more sequences on how to motivate yourself, if I recall there was one written by lukefrog but it wasn't very good.

Hmm I don't think that's a very good description. Rationality means setting rational goals to accomplish what you actually want, and then understanding the world around you and yourself well enough to systematically and logically accomplish those goals. It would certainly include studying yourself to understand how to generate motivation.

I think Dracos been in St. Mungos actually.

This would be if they were stunned immediately on entering the trophy room, like Harry said we don't even know if a duel took place. Granted he could have just waited until after the duel and stunned Draco from behind, both would look the same to us.

Now that I think about it I actually like your way better, cloak and hat is there invisibly and makes sure Draco wins the duel, then stuns Draco while he is leaving. Less work to do with the False Memory charms, less work to do with tampering the wands, and less chance of messing up on evidence since an actual duel was fought.

Hopefully i'm not deluding myself by believing that my solution outlined here is equal or superior to Harry's solution whatever it is.

I outlined my solution here

http://lesswrong.com/lw/axe/harry_potter_and_the_methods_of_rationality/64am

Hermoine is still on the hook in the eyes of Draco and everyone for murder. I believe the story demands a fully vindicated Hermoine to continue, which is why I think Harry will frame Lord Jugson for the false memory charms on Draco and Hermoine. I go into further detail on this elsewhere, just check my comment history.