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New Mexico's least populated corner is this one, which includes the "boot heel" of the Gadsden Purchase, poking 40 miles down toward Mexico (a great place for backpacking). These two railroad towns, an hour apart on I-10, see a lot of traffic; but whereas Deming (pop. 14,500) is thriving as a ranching and retirement center, Lordsburg has had a steady population of about 3,379 for years. This is a popular area for rockhounds, aficionados of ghost towns, and history buffs: Columbus, 32 miles south of Deming, was attacked by the Mexican bandit-revolutionary Pancho Villa in 1916. The U.S. military retaliated by sending 10,000 troops into Mexico to find him, to no avail.