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Combining both the Circulation Strikes and the Proofs for a complete set of U.S. Half Dollars sort of adds the difficult to the impossible, insofar as completeness. You have not only the key dates in the Circulation Strikes such as the 1796-97 Small Eagle reverse, the 1853-O No Arrows, the 1878-S and the varieties (1817/4 and 1806 Knob 6, No Stems) but you also have the early Proofs as well. Most any of the Proofs prior to 1856 will be very tough, and anything prior to 1825 or so will border on the impossible. Nonetheless, almost all the complete denominational series have these difficulties, and that should not dissuade you from putting together one of the most historic and visually interesting sets in the entire registry.
Notes: This set has bonuses. Please see the Set Composition for a listing.