# Euler Problem 9 : Special Pythagorean Triple

## Euler Problem 9 Definition

Scatter plot of the legs (a,b) of the first Pythagorean triples with a and b less than 6000. Negative values are included to illustrate the parabolic patterns. By Dearjean13Own work, CC BY-SA 4.0, Link

A Pythagorean triple 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 of a, b and c.

## Brute Force Solution

This solution uses brute force and checks all combinations of a, b and c. To limit the solution space I used the fact that a < b < c, which implies that a < s/3,  and a < b < s/2, where s is the sum of the three sides.

```a <- 0
b <- 0
c <- 0
s <- 1000
found <- FALSE
for (a in 1:floor((s/3))) {
for (b in a:(s/2)) {
c <- s - a - b
if (a^2 + b^2 == c^2) {
found <- TRUE
break
}
}
if (found)
break
}
answer <- a * b * c
```