Three rings makes perfect sense.
Three Rings for the Elven-kings under the sky, Seven for the Dwarf-lords in their halls of stone, Nine for Mortal Men doomed to die, One for the Dark Lord ...
The Elves have charge of the woodlands, and so a study of their Rings to see which one was used at that time would tell us the culprit.
LOL... Thanks for that! I was trying to come up with something clever related to LOTR, but couldn’t. :)