Marshall,

This is the approach I took when thinking through the problem as well (only I cheated and used excel to lay the events out nicely), by allotting the a,b,c triplet and filling in the 24 sec repeaters and so on. By strictly enforcing a repeating pattern, this does indeed guarantee that each event occurs within the constraints and gives some opportunities for the new event type to occur. The only problem I see with this approach is that it may not be 'optimal' in that the 100s time becomes 96s, the 150s to 144s, though for simplicity's sake this may be the best approach.

And after writing that, I've now done some math and with the tradeoffs of optimization, I'm calculating that in each 24 second 'frame' there would be ~2.21 slots available for a new event type. Without the tradeoffs with a theoretical maximum, I'm calculating ~2.24. I think you've just proven to me that even if it isn't technically optimum, 2.24 and 2.21 are pretty close and this way there are guarantees.