Question 112
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.
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.