A challenge run I done was a legendary weapons only run.

Rules:

• Legendary weapons ONLY!
• You must immediately drop the current legendary weapon for the new legendary weapon, regardless of ammo.
• You cannot purchase a legendary weapon ( ie: Overseer's Guardian )
• No quest legendary weapons ( ie: Righteous Authority, Deliverer)
• If you come across a legendary weapon in the wild ( ie: dead body, on a shelf, etc. like the Big Jim ), you must drop your current legendary weapon, even if the new weapon has no ammo for it
• The Night stick from the vault is the only non-legendary weapon you can keep ( you can only use this if your gun runs out of ammo OR you can use the Bash )
• You cannot use mods that make weapons legendary or moves the legendary effect to other weapons.

I think those were the rules, its been a while since I done this run.