I'm trying to find a way to approach a problem: No two objects can occupy the same slot. Objects can travel 1, 2, or 3 slots per period. There are 18 slots. That is really a very trivial case of a more complex problem. My question is does this sound like similar to any existing problems in mathematics? I'm trying to find a way to analyze the problem (matrix ? modulo arithmetic ?) a simple case follows three objects released at the same time, with rate 1, 2, 3. step1 : 1,2,3 occupied step2 : 2,4,6 occupied step3 : 3,6,9 step4 : 4,8,12 step5 : 5,10,15 step6 : 6,12,18 step7 : 7,14 ... ... ... Eventually I want to analyze a way to, say, maximize objects of any type which traverse the slots over a given number of steps, or how changing number of slots effect the problem. Rather than ask for a solution or analysis, I was wondering if anyone could point me to a similar problem, because I feel like this is a more complex version of a solved problem.