5. Find the largest natural number that cannot be represented as the sum of two composite numbers.

ANSWER: 11
Solution: Even numbers greater than 8 can be represented as the sum of two even numbers greater than 2. Odd numbers greater than 12 can be represented as the sum of 9 and an even composite number. By direct verification, we can see that 11 cannot be represented in such a way.

Lomonosov Moscow State University

## School Olympiad "Conquer Sparrow Hills" in Mathematics

Final stage tasks for the 2015/2016 academic year for grades 5-6

The solutions are similar to those of variant v2a, so only the answers are provided.