Grades 9-10 Video Solutions 2014-Levels 9&10 Video Solutions 2014 problem25

Levels 9&10 Video Solutions 2014 problem25

Video Transcription

Video Summary

Tom needs to avoid the product being divisible by 18, so he avoids numbers divisible by 3 squared (9) or 2. He has two strategies: avoid even numbers, leaving 50 odd numbers (since there are 50 even numbers between 1 and 100), or avoid multiples of 3, leaving 67 numbers (since there are 33 multiples of 3 between 1 and 100). By allowing one even number not divisible by 3 (like 2), Tom can include 68 numbers in his set, ensuring the product is divisible by 2 and 3, but not 18. Therefore, the maximum is 68.

Keywords

divisibility

strategy

numbers

maximum

product