While this is a time-honored "event", the actual FKT is obscure.  The route is about 53 miles, from Hanover to Mt Moosilauke, and is typically done by Dartmouth students at a 24 hour hike supported by the Dartmouth Outing Club.

https://www.dartmouth.edu/~dartmouthdirect/2016/08/the-50-the-ultimate-test/

THE 50. THE ULTIMATE TEST.

When Dartmouth College urges its students to climb mountains, they’re not just being metaphorical.