pe039 - Python

Introduction

pe039 is a Python program that solves Project Euler problem 39. The problem asks for the perimeter of a right-angled triangle (where all sides are integers) that has the maximum number of solutions for all perimeters less than or equal to 1000.

This program implements a brute-force approach to solve the problem by checking all possible combinations of sides for each perimeter value and keeping track of the count of solutions.

Example

To run the program, simply execute the following command in your terminal:

python pe039.py

The program will output the result, which in this case is:

The perimeter with the maximum number of solutions is 840, with a total of 8 solutions.

Explanation

The program first creates a dictionary to keep track of the count of solutions for each perimeter value. It then loops through all possible values of the sides a and b, where a < b and a + b <= 1000. For each combination of a and b, it calculates the corresponding hypotenuse c, and checks whether the resulting triangle is right-angled.

If the triangle is right-angled, the program increments the count for the perimeter value of a + b in the dictionary. After checking all possible combinations of a and b, the program finds the perimeter value with the maximum count of solutions and outputs it along with the count.

Conclusion

pe039 is a simple Python program that implements a brute-force approach to solve Project Euler problem 39. While this approach may not be the most efficient for larger problem sizes, it is still useful for smaller inputs and serves as a good exercise for beginner programmers.