I have just written a solution to the following problem:

we all know the classic "guessing game" with higher or lower prompts. lets do a role reversal; you create a program that will guess numbers between 1-100, and respond appropriately based on whether users say that the number is too high or too low. Try to make a program that can guess your number based on user input and great code!

I would like suggestions on how I can make my solution less complicated and if there is a more efficient way to solve the problem.

Here is my implementation I have tried to implement a binary search strategy to solve the problem.

public class Guesser
{
    private List<int> _possibleAnswers = new List<int>();
    private bool _isCorrectNumber = false;
    private bool _higher = false;
    private int _numberOfGuesses = 0;
    private int _answer;

    public Guesser(int min, int max)
    {
        for (var i = min; i <= max; i++)
            _possibleAnswers.Add(i);
    }

    public void Guess()
    {
        while (!_isCorrectNumber)
        {
            var middleOfAnswers = _possibleAnswers.Max() - (_possibleAnswers.Count / 2);

            Console.WriteLine("Is the number {0}?", middleOfAnswers);

            var hint = Console.ReadLine().ToLower();

            _isCorrectNumber = hint.Equals("yes");

            if (_isCorrectNumber)
            {
                _answer = middleOfAnswers;
                continue;
            }

            _higher = hint.ToLower().Equals("higher");

            if (_higher)
            {
                var count = _possibleAnswers.FindIndex(guess => guess.Equals(middleOfAnswers)) + 1;
                _possibleAnswers.RemoveRange(0, count);
            }
            else
            {
                var startIndex = _possibleAnswers.FindIndex(guess => guess.Equals(middleOfAnswers));
                var count = _possibleAnswers.FindIndex(guess => guess.Equals(_possibleAnswers.Max())) - startIndex + 1;

                _possibleAnswers.RemoveRange(startIndex, count);
            }
            _numberOfGuesses++;
        }
        Console.WriteLine("The number was {0} and it took me {1} guess{2}",
            _answer, _numberOfGuesses, _numberOfGuesses > 1 ? "es" : string.Empty);
    }
}

Any suggestions on how I can improve this would be great and if I have understood the concept behind a Binary search and implemented it correctly.