Medical Mystery

 is a side quest in Fallout: New Vegas.

Walkthrough
The easiest way to complete this quest is to simply wait, hidden, inside/outside the medical tent starting around 1:00 in the morning. Around 2:30, Private Stone will enter/exit, crouched, and attempt to steal the supplies. Depending on your Speech level, you have a number of options in dealing with the situation.

You can also pickpocket Private Stone and take the Empty hydra syringe (the clue) from his inventory. After that, report him to Dr. Richards.

Alternately if you have passed the Medicine check for Dr. Richards to tell you about the symptoms you can talk to Stone by passing another 50 Medicine check, this alleviates the hassle of waiting around 2am for him to sneak into the medical tent. (Stone can usually be found hanging around the barracks)

Another option is to talk to Sexton about missing drug supplies, he'll tell you Stone has been absent from his bunk late at night. Confronting Stone will yield an option to make him confess with a 50 speech check. You can then attempt the 60 speech check to make him turn himself in for a total of 110 XP.

Bugs

 * Private Stone may 'disappear', leaving you unable to complete this quest. The quest marker will point to where he usually 'hangs out' (outside the Command Center), but he's not there. It's possible he's trapped 'underground'. He never appears in the medical tent if this happens.
 * Waiting hidden inside the medical tent between 1:00am and 2:30am can fix this.
 * Reloading to a point before you entered the camp (the first time)and reentering may fix this problem.
 * After the completion of the quest with turning Stone in, he may be absent from the jail and be wandering around still (and stealing the hydra), and all he will say is "Fuck off."