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:
1. Faro Out. Also called the Out riffle shuffle. New order {1,5,2,6,3,7,4,8}.
2. Faro In. Also called the In riffle shuffle. New order {5,1,6,2,7,3,8,4}.
3. Mongean. Move cards alternately to bottom and top. New order {8,6,4,2,1,3,5,7}.
4. Cut. Put half the deck on the other half. New order {5,6,7,8,1,2,3,4}.
5. Hindu. Reverse the order of packets. At size 1, new order is {8,7,6,5,4,3,2,1}.
A perfect shuffling machine is set up to use two of these different shuffle types. When used on 8 cards, out of 40320 possible card orderings, the highest number of different ordering achievable is 192, by using the Mongean and Faro Out shuffles. A table of shuffles on 8 cards is below.
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?
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