- #1
Klungo
- 136
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It's been a while since I've posted. This is a problem I had for a homework assignment a few weeks ago but I completely figure out. Any help appreciated.
"A card-shuffling machine always rearranges cards in the same way relative to the order
in which they were given to it. All of the hearts arranged in order
from ace to king were put into the machine, and then the shuffled
cards were put into the machine again to be shuffled. If the cards
emerged in the order 10, 9, Q, 8, K, 3, 4, A, 5, J, 6, 2, 7, in what
order were the cards after the first shuffle?"
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We have a permutation
[itex]\alpha^2 = \left[ \begin{array}{cc}
A & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & J & Q & K \\
10 & 9 & Q & 8 & K & 3 & 4 & A & 5 & J & 6 & 2 & 7 \end{array} \right] [/itex] which can be written as a single 13-cycle [itex]\alpha^2 = (A,10,J,6,3,Q,2,9,5,K,7,4,8)[/itex].
The goal is to find out how where each card is mapped to under [itex]\alpha[/itex].
And I'm not sure how to go about this.
Homework Statement
"A card-shuffling machine always rearranges cards in the same way relative to the order
in which they were given to it. All of the hearts arranged in order
from ace to king were put into the machine, and then the shuffled
cards were put into the machine again to be shuffled. If the cards
emerged in the order 10, 9, Q, 8, K, 3, 4, A, 5, J, 6, 2, 7, in what
order were the cards after the first shuffle?"
Homework Equations
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The Attempt at a Solution
We have a permutation
[itex]\alpha^2 = \left[ \begin{array}{cc}
A & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & J & Q & K \\
10 & 9 & Q & 8 & K & 3 & 4 & A & 5 & J & 6 & 2 & 7 \end{array} \right] [/itex] which can be written as a single 13-cycle [itex]\alpha^2 = (A,10,J,6,3,Q,2,9,5,K,7,4,8)[/itex].
The goal is to find out how where each card is mapped to under [itex]\alpha[/itex].
And I'm not sure how to go about this.