How to inform a student about my appreciation of his/her original solutions In the final exam of a course, a student has solved some problems in a really ingenious way.
He gets perfect score anyway.
What is the appropriate way to inform him about my appreciation of his solutions?
(Also what if I don't have the occasion to meet him again?)
Just write the student an email and express your appreciation. Don't overthink this. Then again, don't go over the top ("you are the best student I ever had") - you never know how he will take this.

Depending on how well you know the student and on whether you would actually be willing to do so, inform him that you would be happy to write a glowing recommendation for him if he ever needs one, e.g., for admission to grad school.

And as Compass comments, think about how you can help the student develop even further. Do you have any follow-up courses, maybe even advanced ones that the student would usually not take but that you think he would be able to follow? Tell him. Can you give him a research project? Take him on as an Research or Teaching Assistant?



At some point, this turns from "helping the student grow" to "nurturing your own future grad student", and that's OK. This is a mutually beneficial thing, after all. And it's never too early to snap up the promising students. If you don't do it, others will.