Proposed solution to the game for comments and improvements (haven't seen the real one yet)

import random

def helper(a,b,guesses):
  print ('Welcome to the number guessing game written in Python!')
  print ('You will have to guess an integer number within a range [{},{}] with {} guesses'.format(a,b,guesses))

def congrats(number, guesses_counter):
  print ('Congratulations! {} is the correct number'.format(number))
  print ('It took you {} guesses'.format(guesses_counter))

def greater(number, guesses_counter):
  print ('Number {} you entered is greater than the target number. Try again!'.format(number))
  print ('You have used {} guesses'.format(guesses_counter))

def smaller(number, guesses_counter):
  print ('Number {} you entered is smaller than the target number. Try again!'.format(number))
  print ('You have used {} guesses'.format(guesses_counter))

lower_limit = input('>> Provide a lower limit for the number range: ')
higher_limit = input('>> Provide a higher limit for the number range: ')
guesses_limit = input('>> Provide the number of guesses (has to be greater than 0) you want to limit yourself with: ')

a = int(lower_limit)
b = int(higher_limit)
guesses = int(guesses_limit)
guesses_counter = 0

target = random.randint(a,b)

helper(a,b,guesses)

while True:
  number_str = input('>> Try and guess the number between {} and {}: '.format(a,b))
  number = int(number_str)

  if number == target and guesses_counter < guesses:
    guesses_counter = guesses_counter + 1
    congrats(number,guesses_counter)
    break
  elif number > target and guesses_counter < guesses:
    guesses_counter = guesses_counter + 1
    greater(number,guesses_counter)
    continue
  elif number < target and guesses_counter < guesses:
    guesses_counter = guesses_counter + 1
    smaller(number,guesses_counter)
    continue
  elif guesses_counter >= guesses:
    print('You have used all available guesses! Please restart the game!')
    break