As the problem statement says, for each pair of cows $(A, B)$, we will count how many practice sessions cow $A$ did better than cow $B$ in. If cow $A$ did better than cow $B$ in all $K$ practice sessions, we increment a counter, and we'll print out the value of the counter once we've looped over all pairs of cows.

In terms of implementation details, we can use a 2D array to store all of the rankings. Below is Brian Dean's code following this approach.

#include <iostream>
#include <fstream>
using namespace std;
 
int N, K;
int data[10][20];
 
bool better(int a, int b, int session)
{
  int apos, bpos;
  for (int i=0; i<N; i++) {
    if (data[session][i] == a) apos = i;
    if (data[session][i] == b) bpos = i;
  }
  return apos < bpos;
}
 
int Nbetter(int a, int b)
{
  int total = 0;
  for (int session=0; session<K; session++)
    if (better(a,b,session)) total++;
  return total;
}
 
int main(void)
{
  ifstream fin ("gymnastics.in");
  ofstream fout ("gymnastics.out");
  fin >> K >> N;
  for (int k=0; k<K; k++)
    for (int n=0; n<N; n++) 
      fin >> data[k][n];
  int answer = 0;
  for (int a=1; a<=N; a++)
    for (int b=1; b<=N; b++)
      if (Nbetter(a,b) == K) answer++;
  fout << answer << "\n";
  return 0;
}