CS 116 Tutorial 2: Making Decisions in Python

CS 116 Tutorial 2: Making Decisions in Python (Module 2)

Reminders: Assignment 02 is due on Wednesday, January 29 at 10am

Ensure you understand the results of calling choices(8), choices(10), choices(100), choices(111), choices(250),choices(360):

def choices(n):
    answer = 0
    if n % 2 == 0:
        answer = answer + 1
    if n % 3 == 0:
        answer = answer + 1
    elif n % 5 == 0:
        answer = answer + 1
    else:
        answer = 10  * answer
    if n % 10 == 0:
        answer = answer - 1
        if n % 4 == 0:
            answer = answer // 2
        else:
            answer =  2 * answer
    return answer

If you are given three sticks, you may or may not be able to arrange them in a triangle.

If any of the three lengths is greater than the sum of the other two, then you cannot form a triangle. Otherwise, you can. If the sum of two lengths equals the third, they form what is called a "degenerate triangle.”

Write a function is_triangle that consumes three positive integers (s1, s2, and s3) representing the lengths of three sticks and returns one of the following:
- “No triangle exists" if no triangle can be built with the three sticks
- “Degenerate triangle exists" if only a degenerate triangle exists for sticks of these lengths
- “Triangle exists" if a triangle can be made from the sticks
Fermat’s Last Theorem states that given positive integers a, b, and n, there exists no integer c for which a^n+b^n=c^n unless n=2. Although Fermat wrote the statement of this theorem in the margin of a book in 1637, it was not proven until 1995 (and not for lack of trying – thousands of incorrect proofs of the theorem were put forward before it was finally proven).

Write a function fermat_check that consumes four positive integers, a, b, c, and n.
- If n = 2, and a^2+b^2=c^2, then your function should return “Pythagorean triple”.
- If n = 2, and a^2+b^2 is not c^2, then your function should return “Not a Pythagorean triple”.
- If n > 2, and a^n+b^n=c^n, then your function should return “Fermat was wrong!”, as you have found a counterexample to Fermat’s Last Theorem.
- Otherwise, your function should return “Not a counterexample”.
A perfect number is a positive integer that is equal to the sum of its proper positive divisors (i.e. the sum of its positive divisors excluding the number itself).

Write a function is_perfect_num that consumes a positive integer n. The function returns True if n is a perfect number, False otherwise.

For example, is_perfect_num(6) => True (because 1+2+3 = 6).

CS 116: Introduction to Computer Science 2

CS 116 Tutorial 2: Making Decisions in Python (Module 2)