Question 75
Ivan and Peter play the following game. Ivan chooses a secret number from the set $A=\{1,2, \ldots, 90\}$. Then Peter chooses a subset $B$ of $A$ and Ivan tells Peter whether his number is in the set $B$ or not. If the answer is "yes" then Peter pays Ivan 2 leva, and if the answer is "no" then he pays Ivan 1 lev. Find the least amount of leva that Peter needs so that he can always find Ivan's number.