For a deck of six cards, I want to verify that an inshuffle has order $3$ and outshuffle has order $4$.
How do I approach this problem?
2026-03-25 15:41:15.1774453275
Order of shuffled cards and decks
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If original deck $(123456),$ shuffled deck is: $(142356)$ for out shuffle and $(415263)$ for in shuffle. For outshuffle, it is easy to see that 1 & 6 are fixed and the other 4 are involved in a cycle. So, there is one 4 length cycle or the order is 4. For in shuffle, you have 2 3 length cycles. LCM of the cycle lengths (which is order) is 3.