A site which I believe lives up to it’s name! Signing up to Brilliant allows users to join an international community and get free weekly, personalised problems. Questions at various levels are available, including questions suitable for younger students.
Many of the problems such as the one illustrated here would make ideal starters.
Create an account (free) to use the site, or Facebook users can log in easily via Facebook. Once you have signed in you will see a menu option to practice which offers a variety of problems at various levels. If you find a problem you like you can bookmark it. See Lucky Remainder for example or Keep your operations ordered.