Puzzle: Two Shuffles |

Several card shuffles are famous enough that they have been named. From a start of {1,2,3,4,5,6,7,8}, the
new orderings given by one of these shuffles are as follows:

That's 8 cards. For this week, analyze these shuffles for 6 cards. There is one combination of two shuffles that can achieve all 720 different orderings for 6 cards. Which one is it?

- Faro Out. Also called the Out riffle shuffle. New order {1,5,2,6,3,7,4,8}.
- Faro In. Also called the In riffle shuffle. New order {5,1,6,2,7,3,8,4}.
- Mongean. Move cards alternately to bottom and top. New order {8,6,4,2,1,3,5,7}.
- Cut. Put half the deck on the other half. New order {5,6,7,8,1,2,3,4}.
- Hindu. Reverse the order of packets. At size 1, new order is {8,7,6,5,4,3,2,1}.

That's 8 cards. For this week, analyze these shuffles for 6 cards. There is one combination of two shuffles that can achieve all 720 different orderings for 6 cards. Which one is it?