Guess the computer's number using functions

Just some notes:

The bug:

random_number = randint(0, 101)

returns integers from 0 to 101, including both 0 and 101. The fix:

random_number = randint(1, 100)

(but see the next note).

The magic numbers 1 and 100, moreover repeatedly used. You may define them as constants near the top of your code, e. g.

LOWER_LIMIT = 1
UPPER_LIMIT = 100

and then use them in these (inconsecutive) lines of your code:

random_number = randint(0, 101)

print("Simply guess the number between 1-100 that the Computer is 'thinking' of!")

print("Invalid. Enter a number between 1-100 ")

changing them to

random_number = randint(LOWER_LIMIT, UPPER_LIMIT)     # see fix in the first note

print("Simply guess the number between {}-{} that the Computer is 'thinking' of!"
      .format(LOWER_LIMIT, UPPER_LIMIT))

print("Invalid. Enter a number between {}-{} "
      .format(LOWER_LIMIT, UPPER_LIMIT))

( {} in strings are replacement fields for parameters in the .format() method.)

Your answers (Lower... or Higher... ) are ambiguous - is the answer (guess) lower or is such the unknown number?

Maybe something as "Try lower ..." would be more appropriate.

In your congrat_winner() function

def congrat_winner(correct, random_number):
    if correct == random_number:
        print()
        print("Calculating results...")
        sleep(1)
        print()
        print("WELL DONE!")
        print("The answer was indeed,", str(correct) + "!")

is the introductory testing superfluous (and - consequently - the second parameter is needless) as you call that function only after passing the similar test.

So your function may be shortened to

def congrat_winner(correct):
    print()
    print("Calculating results...")
    sleep(1)
    print()
    print("WELL DONE!")
    print("The answer was indeed,", str(correct) + "!")

Subsequently, the part

        else:
            correct = response
            congrat_winner(correct, random_number)

where you call that function have to be changed to

        else:
            congrat_winner(response)      # directly used 'response' instead of 'correct'

(There is no more reason for the correct = response statement.)

I would replace random_number = gen_number() with randint(0, 101).

randint is already a function. What is the use in wrapping it in another function which does nothing extra?

In the loop where you take input you have the following statement:

    try:
        response = int(input(question))
        if response > random_number:
            print("Lower... ")
        elif response < random_number:
            print("Higher... ")
        else:
            correct = response
            congrat_winner(correct, random_number)
    except ValueError:
            print("Invalid. Enter a number between 1-100 ")

If the input is not numeric, you return Invalid. Enter a number between 1-100, but not when your input is outside of the 1-100 range. You might want to add a check for that as well:

    try:
        response = int(input(question))
        if response not in range(1, 101):
            print("Invalid. Enter a number between 1-100 ")
        elif response > random_number:
            print("Lower... ")
        elif response < random_number:
            print("Higher... ")
        else:
            correct = response
            congrat_winner(correct, random_number)
    except ValueError:
            print("Invalid. Enter a number between 1-100 ")

In the last line of your human_guess() function

    guess = ask_number("Guess the number: ", random_number)

you assign the return value of the function ask_number() to a local variable guess which is not accessible from outside of the human_guess() function, so it may be omitted.

So that statement will become just:

ask_number("Guess the number: ", random_number)

Consequently your ask_number() function need not return anything so the last line in its definition

    return response

may be safely deleted, too.

I have collated and considered all the fantastic answers above and greated the following program. I hope this is of significant use.

# Guess My Number Game
# MacOSX (Latest), Python 3.4.3, 28/08/2017
# Guess the Computers number between 1-100

from random import randint
from time import sleep
import sys

LOWER_LIMIT = 1
UPPER_LIMIT = 100

def intro():
    print("""
    Welcome to, Guess My Number!
    Simply guess the number between {}-{} that the Computer is 'thinking' of!
    You will have the option of replaying the game. First, guess the number!

    Ok Human, let's begin... """
    .format(LOWER_LIMIT, UPPER_LIMIT
            ))
    sleep(1)


def ask_number(question, random_number):
    response = None
    while response != random_number:
        try:
            response = int(input(question))
            if response not in range(LOWER_LIMIT, UPPER_LIMIT):
                print("Invalid. Enter a number between {}-{} "
                      .format(LOWER_LIMIT, UPPER_LIMIT))
            elif response < random_number:
                print("Try Higher... ")
            elif response > random_number:
                print("Try Lower... ")
            else:
                congrat_winner(response)
        except ValueError:
            print("Invalid. Enter a number between {}-{} "
                  .format(LOWER_LIMIT, UPPER_LIMIT))


def human_guess():
    random_number = randint(LOWER_LIMIT, UPPER_LIMIT)
    ask_number("Guess the number: ", random_number)


def congrat_winner(winning_guess):
    print()
    print("Calculating results...")
    sleep(1)
    print("CONGRATULATIONS")
    print("The answer was indeed,", str(winning_guess) + "!")


def replay_game():
    replay_question = None
    while replay_question not in ('y', 'n'):
        replay_question = input("Would you like to play again (y/n)? ").lower()
        if replay_question == 'y':
            print("Rebuilding game... ")
            sleep(1)
            main()
        elif replay_question == 'n':
            print("Goodbye... ")
            break
        else:
            print("please enter either 'y' or 'n'... ")


def main():
    intro()
    print()
    human_guess()
    print()
    replay_game()
    print()
    return 0 

if __name__ == '__main__':
     sys.exit(main())