NY Times Puzzle

J711

New Member
#1
Hello new friends. I’m not sure where to post this question so I’ll stay out of the way and start here. The NY Times has a new puzzle callled Letterbox that arranges 3 letters on each side of a square. The object is to make as few words as possible but still use all the letters. Letters can be reused but you must move to another side of the puzzle after a letter is chosen. Here are the rules:

Connect letters to spell words
Words must be at least 3 letters long
Letters can be reused
Consecutive letters cannot be from the same side
The last letter of a word becomes the first letter of the next word
e.g. THY > YES > SINCE
Use all letters to solve!

My question is what is the number of possible letter combinations, ignoring the fact that the combinations must spell words? So if one were to just “brute force” a list of combinations and then “read” through the list to find combinations that are comprised of actual words, how many combinations would there be on the list given the constraints of the puzzle? This is purely hypothetical of course but I think the design of the puzzle is very interesting. Thanks so much.