Hitchcock made a movie, Rope, with exactly 9 cuts, each one only because the film he was using came in 10 minute reels. If you watch it, you will count 4 cuts, the other 5 are disguised with close ups on dark objects such as a man's suit. Edit: I guess technically it's 10 cuts, since the end of the movie is a cut. But maybe I'm just splitting hairs.
Funny that you mention that movie, because I just recently heard of it the other day. They are screening it soon at the Detroit Film Theater, which is the theater associated with the Detroit Institute of Art. I read about it in their flyer, and I plan to see it. Funny the way you avoid something in your consciousness for years then come across it multiple times in a short span. That seems to happen a lot. Maybe it's a matter of just paying attention.