Your task is to implement a number guesser that works on the principle of a binary search. In each step, the guesser cuts the query interval in half. When the interval contains a single number, it proclaims the answer.
Suppose your guesser is asked to guess a number between 1 and 100. It starts with the query
>50
50 is the midpoint between 1 and 100.
The person who knows the number says false. The next query is
>25
25 is the midpoint between 1 and 50.
The answer is still false, and the next query is
>13
The answer is still false, and the next query is
>7
Now the answer is true, and the next query is
>10
The answer is again true, and the next query is
>12
The answer is once again true, and now the guesser proclaims
=13
An object of your class will be called like this:
while (...)
{
   String guess = guesser.nextGuess();
   if (guess.startsWith("="))
   {
      // display answer and terminate loop
      ...
   }
   else
   { 
      // show guess to person who knows the answer
      ...
      // get response from person
      boolean resp = ...; 
      guesser.response(resp);
   }
}