answer:I read the article & watched the video, but I don’t get it. It takes 27 balls to display 12:59 (12 balls on the hours rack, 11 on the 5-min, 4 on the 1-min). But then to roll over to 1:00 would seem to require at least one additional ball “in play,” representing the next minute to trigger the mechanism to dump the racks. That makes 28 balls minimum. Your simulation starts at 27 balls, hence my confusion. When you increase the number of balls where do you put them? Does it simply increase the length of the queue of balls waiting to be scooped up? I think it’s very cool, @phaedryx, that you wrote a simulation program to determine periodicity in the system for variable number of balls. My intuition is that the machine is sufficiently complicated and quirky that there are no simple rules among the numbers you’ve compiled. In other words, your algorithm might be its shortest description!