I have pending post from few months. It is on application of decision trees to analyze algorithms.
"We are provided a two pan fair balance and N identically looking coins, out of which only one coin may be defective. How can we trace which coin, if any, is odd one, and also determine whether it is lighter or heavier in minimum number of trials in the worst case?"
Try to solve the puzzle on your own, and then read my systematic solution on the following link