MathDB

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.

Problem Statement