A medieval king needed to work out how he could recruit fighting men for the battle ahead. However, there were so many distractions around the castle; his thinking became confused. So in order to change his daze into knights, he asked for a secluded walk to be made so that he might ponder in peace. The head gardener was given the job of planting lines of high bushes. First, he planted a line running 100 paces east. Then from the end of that line he planted a line 100 paces north, then 100 west, 98 south, 98 east, 96 north, 96 west, and so on. This made a square spiral path 2 paces wide. If the king intended to walk down the middle of the path, how long was the path?
Answer
The path was 5,000 paces long. If the path is straightened out into a line, its area is that of the square, 100×100 square paces. Dividing by the path width 2 gives the solution.
