How many ARTCC's are there? It appears that the number is 22.

To wit:

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Air Traffic Control Specialist at FAA Air Route Traffic Control Center
The air traffic control specialists at FAA air route traffic control centers give pilots instructions, air traffic clearances, and advice regarding flight conditions along the flight path, while the pilot is flying the federal airways or operating into airports without towers. The controllers use flight plans and keep track of progress of all instrument flights within the center's airspace. She or he transfers control of aircraft on instrument flights to the controller in the adjacent center when the aircraft enters that center's airspace. The controllers also receive control of flights entering his or her area of responsibility from adjacent centers. She or he monitors the time of each aircraft's arrival over navigation fixes and maintains records of flights under his or her control. FAA employs about 6,800 controllers at 22 air route traffic control centers located throughout the US plus one each in Guam, and Puerto Rico.

From: http://umet-vets.dol.gov/air-traffic-control.htm

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What is an "Air Route Traffic Control Center"?
We are one out of 22 Air Route Traffic Control Centers. We control aircraft from the surface up to 60,000 feet. We have over 350 controllers at our facility who work in a radar environment every day. We deal with commercial, military and general aviation aircraft over 174 thousand square miles of airspace.
Another major task that we do is to provide in trail sequencing of arrival aircraft into the Dallas / Fort Worth metroplex as well as provide air traffic services to DFW departures and over flight aircraft. During the past year DFW and Fort Worth Center have modified the way we control aircraft in and out of the DFW area. Our airspace has been modified to provide a major increase to the number of aircraft that can enter and depart from the DFW area. The modification to the airspace is called "The metroplex Plan" and increases traffic flow in and out of the DFW metroplex. DFW airport is now rated the "busiest airport in the world" capable of landing over 132 aircraft per hour in VFR conditions.

From: http://www.zfwartcc.jccbi.gov/faqs.htm