I took a course on Celtic stuffs taught here by Prof. Griffen (who I think has since retired, but may still be reachable if you're interested in pursuing this - his talks were fascinating, btw), and I remember that 3 was a very important number to the celts, with a three-headed (souled) cosmic god, and a triple-aspect goddess (1 soul, three forms: maiden, mother, crone). That particular rule wasn't mentioned, but the idea was that if something happened or was said three times, that made it *real*... (There was also mention of a fourth time, where if something was said a fourth time, it was CEMENTED as truth... or some such.)

Three as a significant number shows up in a lot of mythology, fairy tales, and religions. I bet there's probably a ton of scholarly research on it somewhere, if you know the right search terms. I don't. Google betrays me.