NPCs
First you need a house a (room that fills each requirement). Also each NPC needs a seperate house.
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Lightsource
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Walls and Background walls
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A door
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Tables and chairs
NPC Criteria
You get him at the start and he is only useful for tutorial help and crafting information.
Useful for Piggybank (portable bank slots), Mining helmet (See in the dark)
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Dryad - Must beat a boss (Cthulu, eater of worlds or Skeletron)
Useful for removing corruption and getting seeds.
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Nurse - Player has found a crystal heart.
Useful for healing you for a price.
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Demolitionist - Must found an explosive in your inventory and Merchant needs to be inside a building and not dead.
Sells you explosives (bombs, grenades and dynamite)
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Arms dealer - Must have a gun either from shadow orbs or a chest.
Sells you a gun, ammo and illegal gun parts (1 platinum)
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Clothier - You need to beat Skeletron (Oldman found near a dungeon)
Sells you social items a helmet, mario outfit and black dye.
Extra NPCs you can aquire:
On a Multiplayer map you can get second and even third NPCs
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Second Nurse - Must have 3 players with atleast combined 400 hp in total.
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Second Merchant - 3 players with atleast combined 50 gold
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Third Merchant - 5 players with atleast 5 platinum in total
P.S. not sure what the secondary or the third merchants sell. (Presumably the same items as the first one)