For example, if you climb Grays and then hike over and summit Torreys, you have gained about 3,600 feet and bagged both peaks. If you are intent on gaining 3,000 feet on every peak, Grays and Torreys becomes a completely different task. Hike to the Grays summit, return to the Stevens Gulch trailhead and then start back up to climb Torreys.
Um .... that's not the version I've ever heard before! I've heard the version used by 14ers speed climbers such as Cave Dog:
1. The Colorado Rule:
a) one must ascend at least 3,000 feet in absolute elevation gain on foot from the base of the first peak of a series.
b) foot traverses of less than 3,000 feet are allowed between peaks through traverses.
c) one must descend on foot at least 3,000 feet in absolute elevation loss back to the starting point or end of a traverse.
(From the DogTeam 14ers Rules page; the same idea is described by Roach.)
I wonder how many people on this site that check the "Using the 3k' rule?" box know that it's different than the version Roach cites.