Pattern of Rotation

I have recently re started production of an Old family business of the original Rolling Ball Clock.

http://www.idle-tyme.com

And I just got an E-Mail for someone asking if we have ever tried to determine something.

The clocks motion can be seen at,,

http://www.idle-tyme.com/watch.html

Now the question he asked, is,

say all the ramps are empty, and all the balls are in the reserve track in the back of the clock as seen when the video first starts. So it is now 1 O'Clock. And the Bucket lifting arm grabs one ball from the reserve track and deposits it on the top track so this ball is in the 1 position. So the clock now says 1:01 as the time.

Now we make this ball black so it's obviously different from all the rest.

The question is, how much time or should I say "TYME" must pass for this ball to come back again into this position?

To clarify how the balls are used the arm will continue to grab one ball a minute and deposit it on the top ramp, when the 5th ball is depositited , it overbalances the teter totter and as seen in the video it dumps, the 5th ball takes a different path and it goes now into the middle teter totter in the #5 position, and the other 4 balls go to the right and are stopped by a gate, so at this gate is three silver balls and last in the line is the black ball.

As the bucket arm goes by it raises the gate and lets one ball pass by.

This continues a ball is deposited on the top ramp to now make the time 1:06, and another ball is passed by the gate.

By the time it drops ball 9 then the black ball is released into the lower reserve track.

This pattern of motion continues over and over and over until it is now 1:59, Where the black ball is now located I have no idea, but the middle and top tertotters are full and the next ball from the reserve is being depositited to make the time 2:00

Again the 5th ball on the top terter totter causes it to overbalance and dup out 4 going to the gate again as beforeand #5 ball going to the middle teter totter, but this also now over balances, the 5th ball goes into the bottom one and the remaining balls go to the right like the top one does and get held back by another gate again.

The arm continues to rotate and lets one ball from the top gate pass and then one ball from the middle gate to pass, then pick up the next ball from thr reserve to make it 2:01 for the time.

This all continues on and on and on each hour passes along with the patterns happening all the time.

Now it's 12:59 all the teter totters are full and there are 4 balls left in the reserve.

The bucket scoops up the next ball, that will make the time again 1:00 it drops it on the top ramp and it justlike before over balances all the teter totters, the gates stop the top two teter totters, this ball hits the top one over balancing it, then goes to the middle one and over balances it and then goes to the bottom one making it like 13:00 o clock, and over balances it, and it dumps emptying the ramp and there is no gate to stop this one all the balls pass in a train like stream back into the reserve.

So thats the pattern of operation, and again the question is, How much time will have to pass to have that black ball be again in the top teter totter #1 position. Or even will it ever happen again?

My Brain Hurts even trying to think about this!

Joe