Question

1. The collection of 12 playing cards A♣ K♣ Q♣ A♢ K♢ Q♢ A♡ K♡ Q♡ A♠ K♠ Q♠ is rearranged into the order:

Q♡ Q♢ Q♠ Q♣ K♡ K♢ K♠ K♣ A♡ A♢ A♠ A♣

(a) Do any of the cards stay in the same position as before the re-ordering? Are there two cards that simply swap positions?

(b) Write down the permutation ω, as a cycle or product of cycles, that creates this reordering from the initial given arrangement.

(c) What is the order of ω ?

(d) Is ω an odd permutation, or an even permutation?

(e) If the permutation ω is applied 5 times, what is the resulting arrangement of the 12 cards? Why?

Answer 1

Solution: