Grades 11-12 Video Solutions 2025-2025_11-12

Video Transcription

Video Summary

The problem involves finding the smallest possible maximum among 10 different positive integers, with exactly 5 divisible by 5 and 7 divisible by 7. Using the pigeonhole principle, at least two numbers must be divisible by both 5 and 7, meaning they are divisible by 35. Including numbers like 35 and 70 in our set and filling in the rest with smaller multiples of 5 and 7 creates a valid set of numbers. By minimizing the largest number, the solution satisfies the conditions and identifies 70 as the smallest largest number, which is the edge case given in the problem.

Keywords

smallest maximum

positive integers

pigeonhole principle

divisible by 5

divisible by 7