Medical Mystery

 is a quest in Fallout: New Vegas.

Quick walkthrough
The easiest way to complete this quest is to simply wait, hidden, inside the medical tent starting at ~1:00 in the morning. Around 2:00, a private will enter, 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 empty Hydra (the clue) from his inventory. After that, report him to Dr. Richards.

You can also have 50 in Medicine and ask Dr. Richards about the symptoms of Hydra. After that, confront Private Stones telling him he has the symptoms.

Detailed walkthrough
When you actually find Private Stone trying to sneak his way out, you have several choices:

1) Ignore his movements and let him escape, then report to Dr. Richards. You'll get 300 XP and NCR Fame as a reward.

2) Confront him, let him go and lie to Dr. Richards. It is assumed the 300 XP will remain (more info required)

3) Tell Stone to turn himself in. This requires passing a Speech 60 challenge.

4) Confront him and say you'll let him go if he can make "worth your while". Stone will give you five Hydras for this.

5) You can also turn Stone in even if he gives you the five Hydras. You'll get 300 XP, NCR Fame and a Karma loss for betraying Stone.