How about a game of math and logic puzzles. Ask a logical or mathematical question and if no one can answer within a certain amount of time the asker gives and explain the answer.
I shal go first. This is an older puzzle so some might have heard it before.
A scout infiltrate an enemy camp in order to count the number of cannon balls the enemy has. The enemy has been very helpful and has stacked the balls in a piramid with a square base. each layer of the piramid is of course smaller in square surface as the piramid gets higher until the last layer is only one ball big.
As he watch an enemy soldier aproaches and bring one more ball. Since there is no space for the last ball in this piramid the enemy troops break down the old piramid and build a new one which has a triangular base. In this new piramid the is one spot left on top of the piramid so that the last ball fits exactly.
Before the scout can count however they cover the piramid with a sail and post gaurds. How did the scout compute the number of balls without going near the gaurds.