My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, as well as the input data, too. Or just jump to my GitHub repository.

The code contains #ifdefs to switch between the original problem and the Hackerrank version.
Enable #ifdef ORIGINAL to produce the result for the original problem (default setting for most problems).

       
#include <string>
       
#include <iostream>
       
#include <cmath>
       
 
       
const int NoTriangle = 0;
       
// return triangle index or -1 if not a triangle number

       
int getTriangle(unsigned long long x)
       
{
       
  unsigned long long n = sqrt(2*x);
       
 
       
  // if n it truely the right answer then t(n) = x
       
  unsigned long long check = n * (n + 1) / 2;
       
  if (x == check)
       
    return n;
       
  else
       
    return NoTriangle;
       
}
       
 
       
// read a single word from STDIN, syntax: "abc","def","xyz"

       
std::string readWord()
       
{
       
  std::string result;
       
  while (true)
       
  {
       
    // read one character
       
    char c = std::cin.get();
       
    // no more input ?
       
    if (!std::cin)
       
      break;
       
 
       
    // ignore quotes
       
    if (c == '"')
       
      continue;
       
    // finish when a comma appears
       
    if (c == ',')
       
      break;
       
 
       
    // nope, just an ordinary letter (no further checks whether c in 'A'..'Z')
       
    result += c;
       
  }
       
  return result;
       
}
       
 
       
int main()
       
{
       
//#define ORIGINAL

       
#ifdef ORIGINAL
       
 
       
  unsigned int triangleWords = 0;
       
  while (true)
       
  {
       
    // read next word
       
    auto word = readWord();
       
    if (word.empty())
       
      break;
       
 
       
    unsigned int sum = 0;
       
    // A = 1, B = 2, ...
       
    for (auto c : word)
       
      sum += c - 'A' + 1; // all words contain only uppercase letters without spaces or other characters
       
 
       
    // another "triangle word" ?
       
    if (getTriangle(sum) != NoTriangle)
       
      triangleWords++;
       
  }
       
  std::cout << triangleWords << std::endl;
       
 
       
#else
       
 
       
  unsigned int tests;
       
  std::cin >> tests;
       
  while (tests--)
       
  {
       
    // all work is done in getTriangle()
       
    unsigned long long x;
       
    std::cin >> x;
       
    std::cout << getTriangle(x) << std::endl;
       
  }
       
#endif
       
 
       
  return 0;
       
}

This solution contains 12 empty lines, 13 comments and 6 preprocessor commands.