Here's a puzzle, definitely amenable to computer solution.
I'd like a set of 13 4-letter English words whose letter-sets form a projective plane. So: 1) 13 letters are used in total 2) to make 13 words 3) each word is made of 4 distinct letters 4) each letter occurs in 4 distinct words 5) each pair of words have exactly one letter in common 6) each pair of letters occur jointly in exactly one word
Concrete nouns are preferred.
Is this possible, what sets can you find?