### Instruction: What is the largest number, all of whose digits are 3 or 2, and whose digits add up to $11$?### Response: I want to find a number with the largest possible number of digits, since that would make it larger than any number with fewer digits.
But I also have to make sure that the digits add up to $11$, which is a small sum.
So I want to use as many 2s as possible, since they are smaller than 3s.
If I use five 2s, that would give me a sum of $10$, which is too small.
If I use four 2s and one 3, that would give me a sum of $11$, which is perfect.