$(7)$ Write a function triple riffle$($mylist$)$ which takes as input a list $($which for convenience we will always take with length a multiple of $3)$ and outputs the result of a $3-$way riffle shuffle as described i the lecture notes. For example: an input of range$(9)$ should output $[6,3,0,7,4,1,8,5,2].$

$(8)$ Write a function triple riffle repeat$($mylist$,$n$)$ which takes as input a list $($again with length a multiple of $3)$ and outputs the result of doing a $3-$way riffle shuffle n times.

$(9)$ Write a function period$($m$)$ which takes as input a number m $($which we will always take as a multiple of $3)$ and outputs the smallest positive integer n so that triple riffle repeat$($list$($range$($m$)),$n$)==$ list$($range$($m$)).$

$(10)$ Discuss, with evidence, the outputs of your function period for different values of m$,$ writing your answer as a comment.