A job for the Horn Farm Paste Mob

bit-player asks an interesting question: are there any board positions in Scrabble that are stymied, i.e., in which no additional words can be formed? (Let’s stipulate a two-player game, and that only acceptable words are played. As we know, it’s perfectly legal to invent a word and play it, so long as your opponent doesn’t challenge it; it may be in your opponent’s interest not to challenge a bogus word.) I suspect that such a stymied position, if it exists, uses all four of the S’s. This is actually a two-part problem: find a board position and state of the players’ racks that is stymied, and (harder) find a board position that is stymied no matter how the remaining tiles are distributed.