According to the description shown on Page 234 of the (2013) Red Book, the 1981 Proof Set is supposed to be Type II with a flat "S". Chris
It looks like a mix of Types ?? looks like each set could be all one Type, the other Type or a mix of the two Types ? edited excerpt from, which had a good description https://www.govmint.com/1981-united-states-proof-set Like the 1979-S Proof Set, the 1981-S is found with two types of mintmarks "Round Top and Plato (Flat) Top", with the "Plato (Flat) Top" variety being considerably more valuable than the Round Top. About the sets: All coins in the 1981-S Proof Set were intended to have a Cameo or Deep Cameo Finish. The coins in the 1981-S Proof Set come with two distinctly different mintmarks, known as Type 1 and Type 2. The Type 1 variety (or "Round Top" variety) is actually a worn version of the "Plato (Flat) Top" Type 2 variety of 1979, which had deteriorated by 1981. On the Type 2 variety, the mintmark is clearly defined, and the serifs are separated from the diagonal stroke of the "S". Of the two varieties, the Type 2 "Plato (Flat) Top S" is the more desirable. The most valuable 1981-S Proof Sets are those in which all of the coins are of the Plato (Flat) Top S variety; the value of partial sets drops dramatically, depending on the number of "Plato (Flat) Top S" coins in the set. The Dollar and Cent Type 2 carry the biggest premium. Mintage: 4,063,083 sets
quarter, penny and half are Type 1? dollar, nickel and dime Type 2? .. or the other way around. LOL I can't tell. https://www.coinworld.com/news/precious-metals/type-1-versus-type-2-mint-marks.html edited: full comparison https://www.davescollectiblecoins.com/blog/1979-1981-type-1-2-proof-coins-how-to-spot-them/
It's a mixed set, I see the dollar nickel and quarter as type 2, and the cent, dime , and half as type 1
