1916 D Merc Question

264,000 is actually a darn small mintage for 4 dies; it's not inconceivable that you could get that many strikes from a single pair. Due to revisions and redesigns, the actual mintage of Mercs was not authorized until Oct. 6, 1916. Dies were immediately shipped (or ASAP) and Philadelphia & San Francisco went into full production.

Denver, however, was ordered to mint only Quarters in early November, due to a large order. Note these were Barbers and not SLQ's, the latter having been delayed as well. It was the slowness of the new designs which caused so many Barber designs to be minted in 1916 - it was the original intent of the Mint to produce no Barbers after 1915.

So that's why Denver only minted 264,000 Mercs. As to the total number of dies, I would not be surprised if specific Mint record existed, but I'm guessing the die count is based on physical examination. These aren't really uncommon coins, just very high-demand ones which is the cause of their high price. So, it's been possible for individuals to examine a large number of individual examples, sufficient to draw conclusions about the dies used.