Q: Which would-be state was not allowed to join the United States and lasted only 4 years after its founding? Hint: later, its capitol building mysteriously disappeared.
A: The State of Franklin.
In 1784 North Carolina agreed to cede its westernmost lands to the Union to pay off part of its Revolutionary War debts. The settlers in this territory decided to form an independent state in 1784, and named it the State of Franklin. Delegates of the constitutional convention invited Benjamin Franklin to move there, but he declined. The legislature appointed John Sevier to be the governor. Franklin could have become the 14th state when the United States became a nation in 1787 - but it never did.
Why not? I'm a bit confused about the demise of Franklin. Apparently already in 1784, North Carolina revoked the act that ceded its western territories, but the inhabitants of Franklin refused to rejoin North Carolina, and became rebels. In 1785 the Continental Congress refused to admit Franklin to United States, and the Hopewell Treaty gave southern Franklin to the Cherokees. In 1786 the governor of North Carolina offered a pardon to all Franklin rebels who recanted, but John Sevier did not accept this offer. In 1787 Governor Samuel Johnson of North Carolina ordered Sevier's arrest for treason. One source states that the State of Franklin dissolved in 1788 during a war against the Cherokee, Chickamunga and Chickasaw tribes, and that little is known of the last 15 months of Franklin's history, since only fragmentary records exist.
What used to be the State of Franklin is now Upper East Tennessee. The capital of the State of Franklin was Jonesborough. According to Michael Toomey of the East Tennessee Historical Society, the capitol building of Franklin was taken down to be displayed at the Tennessee state centennial - but when the festivities ended, it had mysteriously disappeared!
However, the key to the front door still exists.
Source: I first heard about the State of Franklin in an interview of Michael Toomey on National Public Radio. You can hear that interview here.
For a quick introduction, try Hank Hayes' article The mystery of the lost State of Franklin, from the archives of The Business Journal of Tri-Cities TN/VA. For a timeline and map, see The Lost State of Franklin, and for more online information, see Internet Resources for the State of Franklin.
There are also various books on the State of Franklin, which I have not read:
For more fun try these: