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The Darkmoon Faire occurs once a month (starting the first Sunday of the month and lasting until the next Saturday).

There are numerous daily quests, in the form of silly games, that you can complete on the Faire grounds for Darkmoon Prize Tickets.  These tickets can be used to purchase a number of things including pets, mounts, heirlooms and transmog gear.

In addition to the daily games, there are monthly quests that will grant you +5 skillups to all primary and secondary professions.  Some of them require additional reagents that you will have to purchase ahead of time:

For Leatherworking bring: x5 Coarse thread, x5 Blue Dye, x10 Shiny Bauble
For Tailoring bring: x1 each of Coarse thread, Red Dye, Blue Dye
For Alchemy bring: x5 Moonberry Juice
For Inscription bring: x5 Light Parchments
For Archaeology, have x15 Fossil fragments gathered.
For Cooking, bring: x5 Simple Flour

Blacksmithing, Engineering, Enchanting, Jewelcrafting, First aid and Fishing do not require any additional materials to complete, nor do the gathering professions Mining, Herbalism, and Skinning.

The following were added to the event in Patch 6.0.2:

Dailies

• Firebird's Challenge (includes achievement reward toy  Blazing Wings)
• A New Darkmoon Challenger! (chance to obtain  Syd the Squid)
  

Items

• These are all sold by Chester

 Last Deck of Nemelex Xobeh
 Haunting Memento
 Nobleman's Coat
 Nobleman's Pantaloons
 Noble's Fancy Boots
 Noblewoman's Finery
 Noblewoman's Skirt

NPC

• Erinys (drops level 100 quest-starter item which rewards  Ring of Broken Promises)