import math

def binary_search_game(): print("Welcome to the Binary Search Guessing Game!")

# Step 1: Get the range of numbers from the user
low = int(input("Enter the lower bound of the range: "))
high = int(input("Enter the upper bound of the range: "))

# Validate the range
if low >= high:
    print("The lower bound must be less than the upper bound. Please try again.")
    return

# Step 2: Calculate the maximum number of attempts needed using binary search
total_numbers = high - low + 1  # total numbers in the range
max_attempts = math.ceil(math.log2(total_numbers))  # Calculate the binary search depth (log2)

# Inform the user about the maximum attempts needed
print(f"\nIt will take at most {max_attempts} attempts to guess a number between {low} and {high} using binary search.")

# Step 3: Start the binary search guessing game
attempts = 0
while low <= high:
    attempts += 1
    guess = (low + high) // 2  # Program guesses the middle number
    
    # Ask the user if the guess is too high, too low, or correct
    print(f"\nAttempt {attempts}: Is your number {guess}?")
    feedback = input("Enter 'higher' if your number is higher, 'lower' if it's lower, or 'correct' if I guessed it right: ").lower()
    
    if feedback == 'correct':
        print(f"\nI found your number {guess} in {attempts} attempts!")
        break
    elif feedback == 'higher':
        low = guess + 1  # The target is higher, so adjust the range
    elif feedback == 'lower':
        high = guess - 1  # The target is lower, so adjust the range
    else:
        print("Invalid input. Please enter 'higher', 'lower', or 'correct'.")

Run the game