BALTIC-WAY 2003 Problem 9

It is known that $n$ is a positive integer, $n \leq 144$. Ten questions of type "Is $n$ smaller than a?" are allowed. Answers are given with a delay: The answer to the $i$ 'th question is given only after the $(i+1)$ 'st question is asked, $i=1,2, \ldots, 9$. The answer to the tenth question is given immediately after it is asked. Find a strategy for identifying $n$.