Write the number N as a multiple of 4's and 5's.

 In equation form:

            N = k1*4 + k2*5               k1, k2 integers

   <==>     k2*5 = N - k1*4

   <==>     k2 = (N - k1*4) / 5
  

 Write the number N as a multiple of 4's and 5's.

            k2 = (N - k1*4) / 5      k1, k2 integers


  int nSols = 0;

  for ( k1 = 0; k1 < N/4; k1++ )
  {
     k2 = (N - k1*4) / 5;          // k2 may not be an integer

     if ( k1*4 + k2*5 == N )
        nSol++;
  }