Design an efficient algorithm to sort 5 distinct keys in fewer than 8 comparisons

Question

Design an efficient algorithm to sort 5 distinct - very large - keys less than 8 comparisons in the worst case. You can\'t use radix sort.

Answer 1

According to Wikipedia:

Determining the exact number of comparisons needed to sort a given number of entries is a computationally hard problem even for small n, and no simple formula for the solution is known."

Presumably this means there is no known tractable (efficient) algorithm for determining an exactly optimal comparison sort.