# Problem 251: Cardano Triplets

![graphic](img251.gif)

A triplet of positive integers (a,b,c) is called a Cardano Triplet if it
satisfies the condition: For example, (2,1,5) is a Cardano Triplet.
There exist 149 Cardano Triplets for which a+b+c ≤ 1000. Find how many
Cardano Triplets exist such that a+b+c ≤ 110,000,000.