A perfect shuffle of a stack of cards involves splitting the stack into two halves of equal size, then alternating cards from the two halves with the bottom card of top half winding up on the bottom of the combined stack. (For example a perfect shuffle of cards labeled 1 through 6 would result in the order 4,1,5,2,6,3.) If you start with a stack of 20 cards, what is the minimum number of consecutive perfect shuffles must you perform so that the cards are back in their original position? (Hint: Turn a perfect shuffle into a permutation.)

A perfect shuffle of a stack of cards involves splitting the stack into two halves of equal size, then alternating cards from the two halves with the bottom card of top half winding up on the bottom of the combined stack. (For example a perfect shuffle of cards labeled 1 through 6 would result in the order 4,1,5,2,6,3.) If you start with a stack of 20 cards, what is the minimum number of consecutive perfect shuffles must you perform so that the cards are back in their original position? (Hint: Turn a perfect shuffle into a permutation.)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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