What is the largest four-digit number whose digits add up to 16?
I want to find the largest four-digit number, so I should start by looking at the most significant digit, the one in the thousands place. To make it as large as possible, I should pick the largest digit that does not exceed 16, which is 9. That means the other three digits must add up to 16 - 9 = 7. The next most significant digit is the one in the hundreds place. To make it as large as possible, I should pick the largest digit that does not exceed 7, which is 7. That means the other two digits must add up to 7 - 7 = 0. The next most significant digit is the one in the tens place. To make it as large as possible, I should pick the largest digit that does not exceed 0, which is 0. That means the last digit must also be 0. So the largest four-digit number whose digits add up to 16 is 9700.

