Question 42
Vika chose a 20-letter word that consists only of letters $A$ and $B$. Oleksii wants to know what Vika's word is. He can ask Vika if there are more $A$'s or $B$'s among several (possibly one) consecutive letters of her word. If there are as many $A$'s as there are $B$'s, Vika's answer may be any of the two letters. What is the least number of questions after which Oleksii can guaranteed determine the word Vika chose?