Project Euler: Problem 9

A Pythagorean triplet is a set of three natural numbers, $a < b < c$, for which,

$$a^2 + b^2 = c^2$$

For example, $3^2 + 4^2 = 9 + 16 = 25 = 5^2$.

There exists exactly one Pythagorean triplet for which $a + b + c = 1000$. Find the product abc.



In [1]:

    
# YOUR CODE HERE
def Pyth_Trip(x):
    #since c>b>a, the limits on b and a can be restricted
    for c in range(0,x):
        for b in range(0,c):
            for a in range(0,b):
                if a + b + c == x:
                    if a**2 + b**2 == c**2:
                        return [a, b, c, a*b*c]

This program takes a few seconds to run



In [2]:

    
print(Pyth_Trip(1000))









    



[200, 375, 425, 31875000]



In [ ]:

    
# This cell will be used for grading, leave it at the end of the notebook.