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EternalStargazer comments on Harry Potter and the Methods of Rationality discussion thread, part 20, chapter 90 - Less Wrong Discussion
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Here's how I would have saved Hermione if I were Harry.
In an accessible but seldom visited hallway of Hogwarts, a rail-way sign reads 6PM to 5PM Express.
At 5:00, a boy materializes under the sign. He is wearing a rail-way conductor's hat. He is holding a trunk. His name is Harry Potter.
Conductor Harry puts down the trunk. He opens the lid. Inside his Trunk of Holding are wooden seats numbered 1 through 1000. All seats appear to be empty.
Conductor Harry yells "Arriving at 5PM! Please add one tally to your forearm now".
Silently, hundreds of people draw a tally mark on their arms.
Conductor Harry steps away from the trunk and the hundreds invisible passengers of the 6PM to 5PM Express disembark.
At 5:10, Conductor Harry closes the trunk lid. He stashes the trunk [EDIT] and Time-Turner in the Great Hall.
At 5:12, Conductor Harry burns his conductor hat. He draws one tally mark on his previously blank arm, and puts on his invisibility cloak. He sighs. He has a long day ahead of him.
...
At 5:30 in the Astronomy Tower, a smelly and disheveled Harry Potter pulls off his invisibility cloak. He is covered with hundreds of tally marks, and looks like he hasn't slept in days. He yells "Screw this, I'm done!", collapses on the floor, and falls asleep.
...
At 5:40, the original Harry goes to his room. He has done no time traveling today, and has no tally marks on his arm.
Original Harry locates his trunk and his conductor's hat.
At 5:45, Original Harry brings his trunk and hat to the hallway with a 6PM to 5PM Express sign.
At 5:50, Original Harry puts on his conductor's hat. Harry -- now Conductor Harry -- opens the trunk, steps aside, and yells "All aboard the 6PM to 5PM Express!. Please go to your assigned seat."
Hundreds of invisible Harrys silently climb into the trunk. Each Harry counts the tallies on his arm and sits in the corresponding seat.
At 5:59, conductor Harry yells "Last Call for the 6PM to 5PM Express!"
At 6:00, conductor Harry closes his trunk. He picks up his trunk, and flips his time-turner.
Using this method, Harry can get as much time as he wants to study obliviation, transfigure large objects, or anything else, all with a single twist of his time turner. That's more than enough time to learn to obliviate yourself (and maybe the Weasley) and fake Hermione's death.
Well, he can get as much time as he wants in 40 minute intervals with no breaks in between. Smelly Harry must have been awake at least 1 hour per mark on his arm, unless he has at some point mastered Polyphasic sleep (which is completely contrary to his aberrant sleep cycles as mentioned previously) he is going to be significantly diminished in terms of mental acuity after a mere 24 or so cycles. He would need to spend a few cycles eating. After subjective days without sleep he should be moving into hallucination territory, barring some kind of magical aid. His "useful time" is only between 5:10-5:50 on each cycle, at other times he will be boarding or leaving the express.
It's a moderately good hack, but it isn't of infinite versatility, barring the addition of a bit more cheating to get around the sleep/food problems.
I think we can let Harry sleep. For example
Instead of drawing a tally mark on his arm, Harry punches a hole in a ticket.
Original Harry doesn't set up chairs in seats 11-20. Instead, he puts a rolling hospital stretcher where chair 11 would go, and leaves 9 empty spots where chairs 12-20 would go. The rolling stretcher has pillows, an empty sleeping bag, and a slot into which you can place a ticket.
When Original Harry moves the trunk to the hallway, he finds 9 stretchers lined up against the wall. Every stretcher has a ticket, and the tickets have 12, 13, 14... 20 hole punches. The stretcher are heavy, like a person is sleeping inside the sleeping bag. Original Harry moves these 9 stretchers into the 9 empty spots he blocked out earlier.
Original Harry puts on his conductors hat and waits for passengers. One of the passengers is Tired Harry, whose ticket has 11 punches. Tired Harry places his ticket into the slot on empty stretcher, climbs into the empty sleeping bag, and goes to sleep. Now all 10 stretchers have ticketed Sleeping Harrys.
On arrival at 5:00, Conductor Harry adds a punch to the ticket of all 10 stretchers. He removes the 10 stretchers from the trunk, and lines the first 9 up against the wall. The last stretcher, with 21 holes punched in its ticket, Conductor Harry stashes in the Great Hall.
At 5:30ish, in the Great Hall, a newly Refreshed Harry wakes up. He gets out of his sleeping bag, picks up his ticket, and continues the day.