Perfect secrecy and block ciphers
It is helpful to first define what a perfectly secure block cipher is. In the ideal case there are n different keys where each key uniquitely indexes one of the permutations mapping {0,1}^k to {0,1}^k. In this case we have n=(2^k)! Possible permutations/keys. 

Perfect security typically means that no information is revealed at all. Not even against an adversary that is computationally unbounded (ie brute force) .

Given such an ideal block cipher (random permutation), can you think of a situation where information is leaked after seeing more than one message. Keep in mind, brute force attacks are allowed here.

Hint, this is why we have block cipher modes.