이틀, 사흘, etc. are the traditional system of counting days. They are all proper names - 틀 or 흘 has no meaning independently. They are used when counting the number of days as a duration, and not to refer to dates except in special cases like the new year(정월 초하루 = 1월 1일). They used to be the main system for both functions but not any more. Here's the list of the names: 1, 하나, 하루 2, 둘, 이틀 3, 셋, 사흘 4, 넷, 나흘 5, 다섯, 닷새 6, 여섯, 엿새 7, 일곱, 이레 8, 여덟, 여드레 9, 아홉, 아흐레 10, 열, 열흘 11, 열하나, 열하루 12, 열둘, 열이틀 ... (likewise add prefix 열 to the single digit ones) 20, 스물, 스무날 21, 스물하나, 스무하루 22, 스물둘, 스무이틀 ... Beyond the low single digit names, they are not used much nowadays. So it's not necessary to know them beyond 스무날.