The 1934 Al Demaree Die-Cut (R304) issue is considered one of the impossible sets to complete. The set is thought to comprise 168 cards, but only 150 are known for certain, and many of those only came to light due to a 109 card discovery in 2009. The set was released in 1934 by Dietz Gum Co. of Chicago, which was owned by Sol Leaf, founder of Leaf Gum some years later. They were intended to be used with a board, which the cards would stand in. The cards are generic drawings (done by former major league pitcher Al Demaree) of players at each position with player photos for the heads. Nine positions plus one batter leads to ten players per team for 16 teams, plus another eight umpires, or a total of 168 cards. (The highest known number is 167.)
The website provides a history of the set.
Al Demaree Die-Cuts (R304) (Set size 168)