Just after throwing a ball (or club or other juggling object), all balls are in the air and are under the influence of gravity. Assuming the balls are caught at a consistent level, then the timing of when the balls land is already determined. We can mark each point in time when a ball is going to land with an "x", and each point in time when there is not yet a ball scheduled to land with a "-". This describes the current state and determines what number ball can be thrown next. For instance, we can look at the state just after our first throw in the diagram, it is xx--x. We can use the state to determine what can be thrown next. First we take the "x" off the left hand side (that's the ball that's landing next) and shift everything else to the left filling in a "-" on the right. This leaves us with x--x-. Since we caught a ball (the x we removed from the left) we can't "throw" a 0 next. We also can't throw a 1 or a 4, because there are already balls scheduled to land there. So assuming that the highest we can accurately throw a ball is to a height of 5, then we can only throw a 2, 3, or a 5. In this diagram, the juggler threw a 3, so an x goes in the third spot, replacing the -, and we have x-xx- as the new state.