Wall king

A king likes to walk. He instructs his gardener to plant hedges to build a spiral in which he can walk. The gardener starts with three sides of a square, each 100 of the king's paces long. On the fourth side of the square, he plants a hedge only 98 paces long. He then plants another 98-pace hedge into the original square, and continues a square spiral toward the center, always leaving a 2-pace width for the king to walk in. If the king walks along this path from the outside to the center of the maze, how far does he walk?


draw a diagram

add up lengths, perhaps using young Gauss's method

multiply each length by 3, then add

multiply each length by 2, then add

consider whether the king walks the inner edge or the middle

think about when the king turns

imagine stretching out the maze

Your experience

Have you used this problem with a class and seen approaches other than(or more specific than) those mentioned above? Or do you have other comments or criticisms or stories? If so, please tell us!

Last updated 30 November, 2004