7.4. Find the smallest natural number with the sum of its digits equal to 2014.
Answer: 799... 9 (223 nines). Solution. This answer is intuitively clear: you need to use as many nines as possible, and write the missing digit to 2014 first. Let's justify this strictly. If the desired number had fewer than 224 digits, the sum of the digits would not exceed $223 \cdot 9=2007$; if the first digit of the 224-digit number was less than 7, the sum of the digits would not exceed $6+223 \cdot 9=2013$