How a Nerd Walks Up the Stairs

Your steps should be in a cycle: short, long, long. Long in this case means a double step. Thus, you will cover five stairs in one short-long-long cycle. In addition, you should always start the first cycle on the same foot. Suppose you start on the left foot, then after two cycles you are back on the left foot, having covered ten stairs. While you are walking the stairs in this way, it is clear where you are in the cycle. By the end of the staircase, you will know the number of stairs modulo...