Nuzzles is a web puzzles game for kids, completely clean of annoying ads and other distractions. It's designed for desktop and mobile devices (note: recommended to use fullscreen mode so your kid won't accidentally exit page) and have simple UI kids can use.

I made this small project as a gift for my daughter when she was three. 
Source code can be found here: https://github.com/RonenNess/Nuzzles