Here is a very famous logic problem:

The Emperor's Banquet

"You have been invited to the Emperor's banquet. The Emperor is a rather strange host. Instead of sitting with his guests at his large, round dining table, he walks around the table pouring oatmeal on the head of every other person! He continues this process, pouring oats on the head of everyone who has not had oats until there is only one person left. You will know when you arrive where the first seat is to get the oats and that the Emperor always rotates to the left with his oats. You do not know in advance how many people will be there. Devise a system that will tell you in what seat to sit in order to not get 'oatmealed' once you know how many people are at the banquet."

See if your kids can figure out this problem.