Track / Stage 4 / 87 of 340 #347 of 1964

Problem 347

AMC 12 late, AIME early

Number theory Difficulty 4.7 Find the answer

Let $n$ be the smallest positive integer such that the sum of its digits is 2011 . How many digits does $n$ have?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

17. Answer: 224 .
For smallest possible $n$ , we need to have 9 as the digits of $n$ as many as poesible. So $n$ is the integer whose first digit is $2011-223 \times 9=4$ and followed by 2239 's.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.