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

**Commentary:** I’m not proud of this solution. Every time I would look
at this solution, I just knew there was something really obvious I was
missing–that I was doing this in the most bone-headed way possible. So
then I finally just gave up and checked the writeup at Project Euler,
and yep, I forgot that Pythagorean Triplets have a very nice
parametrization.

I won’t even bother to reproduce the idea here, because the writeup over at Project Euler is actually very well done. But it is a bit embarrassing to have a masters in number theory and to forget that simple fact. Oh well.

**R Code:**

```
ElapsedTime <- system.time({
##########################
for (a in c(1:333)){
for (b in c(334:998)){
test <- a+b+sqrt(a^2+b^2)
if (test==1000){
win.a <- a
win.b <- b
break
}
}
}
answer <- win.a*win.b*sqrt(win.a^2+win.b^2)
##########################
})[3]
ElapsedMins <- floor(ElapsedTime/60)
ElapsedSecs <- (ElapsedTime-ElapsedMins*60)
cat(sprintf("\nThe answer is: %d\nTotal elapsed time: %d minutes and %f seconds\n", answer, ElapsedMins, ElapsedSecs))
```

**Output:**

****The answer is: 31875000
Total elapsed time: 0 minutes and 0.460000 seconds