Grades 9-10 Video Solutions 2010-Levels 9&10 Video Solutions 2010 problem27

Levels 9&10 Video Solutions 2010 problem27

Video Transcription

Video Summary

The problem involves labeling a pentagon with natural numbers such that adjacent sides share a greatest common divisor (GCD) of 1, while non-adjacent sides have a GCD greater than 1. The strategy is to avoid using prime numbers for the labeling, as these fail the non-adjacent requirement. For instance, labeling a side with a prime number like 11 leads to non-adjacent sides having GCD of 1 when the other number is less than 11. This violates the condition that non-adjacent sides must have a GCD greater than 1. Therefore, prime numbers cannot be labels, and 11 cannot be used.

Keywords

pentagon labeling

greatest common divisor

natural numbers

prime numbers

non-adjacent sides