There are 134 FBS football teams spread across 41 states. Of the nine states without an FBS team, 7 have one or more FCS teams. The exceptions are Alaska and Vermont. Alaska had the University of Alaska Polar Bears in the mid-1950s, so they qualified as one of a handful of states with college football before statehood.
Vermont, on the other hand, has college football teams competing at lower levels today. Also, the University of Vermont had a football team from 1886 to 1974, when it ended its program as a member of the Yankee Conference, playing the equivalent of today's FCS. That makes UVM the only state flagship school to play and drop football.
The program did not start well, losing its first game, 99-0, to Dartmouth. Most years, its schedule was dotted with regional state schools and small colleges, and it did not fare particularly well regardless of its foe.
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