Problem:
Given that
2!17!1​+3!16!1​+4!15!1​+5!14!1​+6!13!1​+7!12!1​+8!11!1​+9!10!1​=1!18!N​
find the greatest integer that is less than 100N​.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions