Finding the Pythagorean Triplet: Project Euler Problem 9

The Challenge

Project Euler Problem 9 asks us to find the unique Pythagorean triplet where a + b + c = 1000, then calculate the product abc.

A Pythagorean triplet consists of three natural numbers a, b, c where:

• a² + b² = c²

• The classic example being 3² + 4² = 5² (9 + 16 = 25)

The Brute Force Approach

The solution above takes a straightforward nested loop approach:

python

import math
for a in range(0,1000):
    for b in range(0,1000):
        for c in range(0,1000):
            if a < b < c:
                if (a * a) + (b * b) == (c * c):
                    if a + b + c == 1000:
                        print(a * b * c)

This works by:

1. Testing all possible combinations of a, b, and c from 0 to 999

2. Ensuring proper ordering (a < b < c)

3. Checking the Pythagorean theorem condition

4. Verifying the sum equals 1000

The Result

Running this code finds: a = 200, b = 375, c = 425

The product: 200 × 375 × 425 = 31,875,000