Consider the following quicksort-like sorting algorithm. Pick two elements of the list. Partition based on both of the elements. So the elements smaller than both are to the left, the elements in between are in the middle, and the elements larger than both are to the right.

Assume that the two partition elements always partition so exactly one quarter are to the left, one half in the middle, and one quarter to the right. Write a recurrence for the number of comparisons. Solve this recurrence using constructive induction. Just get the high order term exactly.