graff: kcott raised the most important points. To expand on that a bit...

Kind sorta almost ... the question/problem feels more at the fizz-buzz stage, the OP has a good idea (almost) its just translating it into code, and working through the hurdles, thats the issue

For example, if he can get $max to affect add_max ... then notice the issue with the update you mentioned

then its just a matter of adding a update limit clause