BALKAN-SL 2015 C2

Isaak and Jeremy play the following game. Isaak says to Jeremy that he thinks a few $2^n$ integers $k_1,..,k_{2^n}$ . Jeremy asks questions of the form: ''Is it true that $k_i<k_j$ ?'' in which Isaak answers by always telling the truth. After $n2^{n-1}$ questions, Jeramy must decide whether numbers of Isaak are all distinct each other or not. Prove that Jeremy has bo way to be ''sure'' for his final decision.

(UK)