For weekly problems try the challenges from the University of Mississippi.
Four problems are set every week.
The Problem of the Week and Algebra in Action challenges are open to anyone from anywhere of any age! The Middle School Madness and Elementary Brain Teaser problems are for school age children, Middle School Madness for grade 8 (age 14 and under), the Elementary Brain Teaser for grade 6 (age 12 and under). If you submit a correct solution by the deadline that week your name will be published on the website. You might even win a T-shirt!
I have posted details for students here.