Grades 11-12 Video Solutions 2011-11&12 Video Solutions 2011 problem29

11&12 Video Solutions 2011 problem29

Video Transcription

Video Summary

In a 4x5 grid filled with 20 different positive integers, each pair of neighboring cells must share a common divisor greater than 1. The objective is to determine the smallest possible largest number, denoted as \( n \). By systematically evaluating lower values of \( n \) and the required inclusion of certain multiples that disrupt the conditions, it is shown that any attempt to reduce \( n \) below 26 involves using prime numbers or their multiples that don't satisfy the grid's constraints. Thus, the smallest possible \( n \) for which the grid's rules hold is 26.

Keywords

grid

positive integers

common divisor

smallest number

constraints