Do not describe the randomized algorithms or provide conceptual background on random algorithms. Simply provide a counter example to the proposed question.

Dr. Smart argues that because the randomized algorithms (such as Gibbs sampling algorithm) can identify the motifs consisting one k-mer in each input sequence, the consensus of these k-mers should be always the median string of the same set of input sequences. Is he correct? If yes, explain why. If not, can you give a counter example (i.e., where the consensus of the identified motifs is NOT the median string of the input sequences)?