CareerCup

Solution in python

def compute_interesting_times(s, t):
    def convert_number(x):
        pad = ''
        if x < 10:
            pad = '0'
        return pad + str(x)
        
    # Check times
    if s > t:
        raise ValueError("The init time is greater than the finishing time")
        
        
    # Parse times
    h_c, m_c, s_c = map(lambda x: int(x), s.split(':'))
    h_f, m_f, s_f = map(lambda x: int(x), t.split(':'))
    total = 0
    
    while not (h_c == h_c and m_c == m_f and s_c == s_f):
        # Transform the numbers into a proper string and
        # check if we have to increase the total
        a = '{}{}{}'.format(convert_number(h_c),
                            convert_number(m_c), 
                            convert_number(s_c))
        if len(set(a)) <= 2:
            total += 1
        
        # Update the time counters
        s_c += 1
        if s_c == 60:
            s_c = 0
            m_c += 1
            if m_c == 60:
                m_c = 0
                h_c += 1

    # Check if the finishing time is an interesting time
    a = '{}{}{}'.format(convert_number(h_c),
                            convert_number(m_c), 
                            convert_number(s_c))
    if len(set(a)) <= 2:
        total += 1

    return total

/*
Essentially - generate a date-time range,
with spacing of 1 sec, each,
and then check if the string rep has 2 or less unique chars.
That is how one does a fully declarative coding.
Observe : en.wikipedia.org/wiki/ISO_8601
*/
def compute_interesting_times( s1, s2 ){
  input_time_format = 'HH:mm:ss'
  time_range = [ time(s1,input_time_format) : time(s2,input_time_format) + 'PT1S' : 'PT1S' ]
  output_time_format = 'HHmmss'
  x = select( time_range ) where {
     s = str($.o, output_time_format)
     size(set(s.value)) <= 2
  }
  size(x)
}
println( compute_interesting_times("15:15:00", "15:15:12") )
println( compute_interesting_times("22:22:21", "22:22:23") )

in one full hour we have 16 interesting times: two digits in four positions (2^4)
in one full minute we have 4 times 2^2, just need to count full hours, full minutes and take on partial hours and minutes