Track / Stage 4 / 75 of 340 #335 of 1964

Problem 335

AMC 12 late, AIME early

Number theory Difficulty 4.7 Find the answer

17. 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. Spacing and $ signs are ignored.

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 and solution reproduced as published; topic, difficulty and ordering added by this site.