I'm sure he knew exactly what was going on, and as someone else has mentioned he probably heard it aswell, but simply chose to turn a blind eye because he wanted to get Private Pyle on the same level as everyone else.
Don't put the devil in the picture, cause' the religious groups won't wanna see it.

Hartman would not have issued a formal order. He incited them to do a "Code Red", but formally ordering them to beat up a fellow recruit would have been illegal and he would not want to be court-martialled.
"Chicken soup - with a beep straw."

Whos to say that the privates, or at least some of them, were not ordered by Hartman to do so? In any event, they were working together as a team which is probably why Hartman didnt intervene. Drill instructors and drill sergeants know everything that goes on in the barracks. Hartman knew about this

Exactly.

He wanted them to "motivate" Pyle. Why would he intervene?
"Chicken soup - with a beep straw."

Hartman probably did hear it, but he had punished the other recruits for not helping him motivate Pyle. They were finally applying some motivation, so he did not respond to what he heard.

I don't see how Hartman didn't hear Pyle crying out in pain. Didn't Hartman sleep in the same barracks, but in a private room?

Even if Hartman expected them to give him a blanket party like they did he would be obliged to deal with it if he personally witnessed it taking place, otherwise he risks being reported to his superiors for allowing assaults to happen on his watch and command and doing nothing when he sees them happening, highly illegal, he might want them to motivate Pyle late at night and whip him into shape but he cant see it happen and not do anything either, it looks bad and other drill instructors that are more by the book and not corrupt enough to allow such things would hear and report him for his corrupt training.
Personally i dont know why Pyle didnt run to Hartman the next day and report what happened to him, explain how he was assaulted by everyone with towels and soap wrapped in them, how he was injured and didnt deserve it, just basically tell on them and rat them all out to Hartman, not knowing that Hartman wanted them to do it to him, Hartman cannot ignore a recruit that reports that they have been assaulted by other recruits, but he also cannot punish the entire unit or maybe he can, that would make Pyle even more hated and unpopular than ever.
A second blanket party could happen as a result of that, with a warning not to tell on them again or he gets a proper ass kicking next time, or maybe they would just kick his ass and beat him good, but that would require an official investigation and would probably backfire.

I think Hartman sort of expected them to do it - egging them on a bit with the whole jelly donut scene.
Buy The Ticket, Take The Ride

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