## Cardano Triplets

### Problem 251

Published on Saturday, 20th June 2009, 09:00 am; Solved by 851; Difficulty rating: 70%
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.