Very simple guessing game, to demonstrate binary search. Select a bound, and choose for yourself a number within that bound.

bsearch_game.py

def which() -> str:
    print(f'1) Correct!\n2) My number is smaller.\n3) My number is bigger')
    while True:
        res = input('Type 1, 2 or 3: ')
        if not res.isdecimal() or int(res) not in (1, 2, 3):
            print('Invalid input!')
            continue
        break
    return ['correct', 'smaller', 'bigger'][int(res) - 1]


def main():
    lower_bound = int(input("Enter the lower bound: "))
    upper_bound = int(input("Enter the upper bound: ")) + 1

    guesses = 0
    while lower_bound < upper_bound:
        mid = (upper_bound + lower_bound) // 2
        print(f'Is our number {mid}?\n')
        guesses += 1
        result = which()
        if result == 'correct':
            print(f'So your number is {mid}! I got it in {guesses} guess{'es' if guesses != 1 else ''}!')
            break

        if result == 'smaller':
            # users number is smaller
            upper_bound = mid
        else:
            lower_bound = mid
        print()
    else:
        print('Hmm... it seems I missed your number?')


if __name__ == '__main__':
    main()