Lecture Notes on 13 Feb 2017

Active Reading: Type code as you read.

Read Chapter 6: Sections 6.1 - 6.6

Write the code from the following listings and run them:

* Listing 6.1: TestMax.py

* Listing 6.2: PrintGradeFunction.py

* Listing 6.3: ReturnGradeFunction.py

* Listing 6.4: Increment.py

Challenge Problem:
Imagine you are standing in front of a long hall way that has 500 doors. Each
door is numbered starting from 1 and ending at 500. All the doors are closed.
There are also 500 persons numbered from 1 to 500. The first person comes and
opens all the doors. The second person starts at door number 2 and visits all
the even doors and closes them.

The third person starts at door number 3 and visits all the doors that are
multiples of 3. If the door is open he closes it. If a door is closed he
opens it. The fourth person starts at door number 4 and visits all the doors
that are multiples of 4 and he closes open doors and opens closed doors.

After all 500 people have gone through the hallway, how many doors are still
open?

# sum the digits of a number
def sum_digits (n):
  sum_num = 0
  while (n > 0):
    sum_num += (n % 10)
    n = n // 10
  return sum_num

# sum the proper divisors of a number
def sum_divisors (n):
  sum_div = 0
  limit = n // 2
  div = 1
  while (div <= limit):
    if (n % div == 0):
      sum_div += div
    div += 1
  return sum_div

# reverse a number
def rev_num (n):
  rev_n = 0
  while (n > 0):
    rev_n = rev_n * 10 + (n % 10)
    n = n // 10
  return rev_n

# determines if a number is palindromic
def is_palindromic (n):
  return n == rev_num(n)

# determine if a number is prime
def is_prime (n):
  if (n == 1):
    return False

  limit = int (n ** 0.5) + 1
  divisor = 2
  while (divisor < limit):
    if (n % divisor == 0):
      return False
    divisor += 1
  return True

def main():
  # prompt the user to enter a number
  num = int (input ("Enter a number: "))

  # print the sum of the digits
  print (sum_digits(num))

  # print sum of the proper divisors
  print (sum_divisors (num))

  # print the reverse of a number
  print (rev_num (num))

  # print all perfect numbers less than 10000
  n = 1
  while (n <= 10000):
    if (n == sum_divisors (n)):
      print (n)
    n += 1
 

main()