A very popular hike is to make a loop combining the three most notable summits of the Franconia Range. The loop starts with the Old Bridle Path to the AMC Greenleaf Hut. From there, one takes the Greenleaf Trail to the summit of Mt. Lafayette. Turning south along the Franconia Ridge Trail, one passes over Mount Lincoln and Little Haystack, then descends via the Falling Waters Trail, which connects back with the beginning of the Old Bridle Path. This loop is 8.9 miles (14.3 km) long, with a cumulative elevation gain of about 3,900 feet (1,200 m). (copied from Wikipedia)
The scouts did this loop in the reverse direction.