SOLUTION: Classify whether the permutation is odd or even. a. [1 2 3 4 5 6 7 8 3 1 5 2 4 7 8 6 ] b. [1 2 3 4 5 6 7 8 1 3 5 6 2 7 8 4 ] c. [1 2 3 4 5

I'll just do the last one.

c. [1 2 3 4 5 6 7 8] 
   [3 4 1 5 2 7 8 6]

We determine the orbits:
1->3->1
So the first orbit is [1 3]
2->4->5->2
So the second orbit is [2 4 5]
6->7->8->6
So the third orbit is [6 7 8]

So the permutation is [1 3][2 4 5][6 7 8]

Writing it two ways as a product of tranpositions:

[1 3][2 5][2 4][6 8][6 7]
or
[1 3][2 4][2 5][6 7][6 8]

There are 5 transposition in the product, and 5 is 
odd, so the permutation is odd.

Edwin