This is a simple bin-packing problem with weights = 1

 The solution is:

    (1) sort the durations

          3 3 3 6

    (2) pack - starting with the small one to large - 
        as many as you can into T
  

   cin >> T;  // # mins (time)
   cin >> C;  // # chores

   int t[C];  // Store times of each chore

   for ( int i = 0; i < C; i++ )
      cin >> t[i];

   sort (&t[0], &t[C]);  // Sort the times of chores from low to high

   /* ================ Solve J4 =================== */
   int k = 0;    // # chores done so far
   int sum = 0;  // # minutes needed

   while ( k < C && sum < T )
   {  // Try to do the next chose

      if ( sum + t[k] <= T )
      {
         sum += t[k];
         k++;
      }
      else
         break;   // Out of time, done.
   }

   cout << "Answer: " << k << endl << endl;