Unlock the Armory

 is an unmarked quest in Fallout.

Walkthrough
If your character has a moderate Intelligence and a good Speech skill then go to the armory on level three of Vault 13 (the locked door with the red light). Speak to the Vault 13 Officer and tell her that you need more ammunition and then ask who has access. You'll then get the option to say that "it sounds like only the people who need it have access" and then that you "have need". If you can persuade her she will open the armory door for you.

Reward
Inside the armory:
 * Shotgun.
 * 12 gauge shotgun shells.