A clue " k digits, sum is n " gives a number k and the sum of k distinct, nonzero digits. An answer for that clue consists of k digits with sum n. For example, the clue "Three digits, sum is 23 " has only one answer: 6,8,9. The clue "Three digits, sum is 8 " has two answers: 1,3,4 and 1,2,5.
If the clue "Four digits, sum is n " has the largest number of answers for any four-digit clue, then what is the value of n? How many answers does this clue have? Explain why no other four-digit clue can have more answers.