2020-18 A way of shuffling cards

Consider the cards with labels \( 1,\dots, n \) in some order. If the top card has label \(m \), we reverse the order of the top \( m \) cards. The process stops only when the card with label \( 1\) is on the top. Prove that the process must stop in at most \( (1.7)^n \) steps.

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