The Christmas Tree Puzzle is a fabulous online site for problem solving and critical thinking. The goal is to light up the Christmas tree by connecting all the wires to the light source. It's lots of fun but it is definitely a challenge that requires lots of problem solving.
This would be a fabulous whole class activity using your Smartboard. It would be great for both younger students who would most likely apply the trial and error method, and for older students who would come up with a strategy to accomplish the task.