Question 14
An infinite strip has one ball per square and a periodically repeated permutation $a_1\ldots a_n$ of $1,\ldots,n$, $n\ge3$. Each ball jumps right by the number written in its starting square. A pattern is collision-free if no square receives two balls. The patterns 123,231,312 are collision-free; 213 is not. Cyclic shifts represent the same pattern, so for n = 3 there is one pattern. How many collision-free patterns exist for n = 5? Give a complete explanation; merely listing the patterns is insufficient.
