Rachael Sharp edited In_general_if_we_wish__.tex  about 8 years ago

Commit id: 6bead560777a21228955b86c5275eaad6c7f6071

deletions | additions      

       

$(11)$  Each number that follows describes what position that card will be moved to and it ends when the cycle would repeat. For whatever size deck, every card needs to be represented. If one value has not made an appearance in the previous sets, you must start a new set.  Notice that the first card, $0$, and the last card $11$ do not move. This should be expected as this is what characterizes an out-shuffle. Through this, you can also find the number of out-shuffles it will take to return to the original order. Notice that there are three sets of patterns. In the first, there is one value, in the second there are ten values, and in the last there is one value. The least common multiple of the sizes/lengths of each set will describe the number of shuffles needed. In this case, we have lcm($1,10,1$)=$10$. So it takes ten out-shuffles to return a deck of size $12$ back to the original order.