I had a similar issue. I was guessing "is it after <year>", "is it rated <r/pg-13/PG/g>", "is it a comedy", "does it have romance", then tried binary searching for the first letter. I asked if it started with the letter A, and got this:
Congratulations you guessed the movie!
Your score was 500
Congratulations! The movie starts with the letter "A". Keep guessing!