int findArithSeqs(int nMins) // Find # Arithm Seqs within nMins minutes
{
   int nSeqs = 0;
   int hr    = 12; // Start at 12:00
   int min   = 0;

   // Check every reading of the digital clock
   for ( int i = 0; i < nMins; i++ )
   {
      min++;  // This can make min >= 60 !
      adjust  hr, min  to HH:MM, where 1 < HR < 12, 1 < MM < 59

      if ( hr < 10 )
      {
         Time = a:bc
         if ( a, b, c is an arithm. seqs )
            nSeqs++;
      }
      else
      {
         Time = ab:cd
         if ( a, b, c, d is an arithm. seqs )
            nSeqs++;
      }
   }
   return nSeqs;
} 

int findArithSeqs(int nMins) // Find # Arithm Seqs within nMins minutes
{
   int nSeqs = 0;     // # arithm seqs found

   /* --------------------------------------------------
      Start time at 12:00
      -------------------------------------------------- */
   int hr = 12;       // hr and min simulate the 12 hr clock...
   int min = 0;

   int a, b, c, d;    // a,b,c,d are the digits on the clock...


   /* ---------------------------------------------
      Check time from 12:00  to 12:00 + nMins
      --------------------------------------------- */
   for ( int i = 1; i <= nMins; i++ )
   {
      min++;            // next time in minutes

      // Adjust clock
      if ( min == 60 )
      {
         hr++;
         if ( hr == 13 )
            hr = 1;
         min = 0;
      }

      // Check for arithm. seq
      if ( hr < 10 )
      {  // Time is 3 digits

         a = hr; b = min/10; c = min%10;

         if ( (a-b) == (b-c) )
         {
             nSeqs++;
         }
      }
      else
      {  // Time is 4 digits

         a = hr/10; b = hr%10; c = min/10; d = min%10;

         if ( ((a-b) == (b-c)) && ((a-b) == (c-d)) )
         {
             nSeqs++;
         }
      }
   }

   return nSeqs;
} 

 Observe that the digital clock is periodic:

    12:00 --> 1:00 --> 2:00 --> .... --> 11:00 --> 12:00 --> 1:00 ...


 Each period is 12 hrs = 12*60 mins


 12:00
   |---------------------------------------------------------------|
    <--------------------------- D mins -------------------------->

 12:00          12:00          12:00          12:00          12:00
   |--------------|--------------|--------------|--------------|---|
                                                                 R

         D = #periods + R

         # periods = D/(12*60)
         R         = D%(12*60)

 So:

     findArithSeqs(D) = D/(12*60) * findArithSeqs(12*60)
                        + findArithSeqs(D%(12*60))