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.)

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.5: Counting Principles

Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...

See similar textbooks

Similar questions

How many ways can a committee of 3 freshmen and 4 juniors be formed from a group of 8 freshmen and 11 juniors?
A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in the front and 3 in the back a. How many arrangements are possible with no restrictions? b. How many arrangements are possible if the parents must sit in the front? C. How many arrangements are possible if the parents must be next to each other?
Alice and Bill have four grandchild, and they have three framed pictures of each grandchild. They wish to choose one picture of each grandchild to display on the piano in their living room, arranged from oldest to youngest. In how many ways can they do this?
A hospital cafeteria offers a fixed-price lunch consisting of a main course, a dessert and a drink. If there are four main courses, three desserts, and six drinks to pick from, in how many ways can a customer select a meal consisting of one choice from each category?
Over the past year, John has purchased 30 books. In how many ways can he pick four of these books and arrange them, in order, on his nightstand bookshelf? In how many ways can he choose four of these books to take with him on his vacation at the shore?