Solving Maze Puzzles
Sidney Kravitz · Mathematics Magazine · 1965
Several years ago a puzzle contest was sponsored for advertising purposes. Each contestant was required to solve a series of increasingly difficultmaze puzzles of the type described below. Following in the footsteps of Euler's Seven Bridges of K6nigsberg [1] a method is presented for solving these puzzles. A simple example of the type of puzzle referred to is shown in Figure 1. Here we see several areas (marked by small circles and identified as a, b, c, h, i), with each area given a numerical value (not shown). The contestant is required to trace a route between the starting point (marked S) and the final point (F) using only the paths shown (as dashed lines) and passing through each area no more than once. Numerical credit is given only for those areas which the route passes through. The contestant who achieves the highest numerical sum wins. Let us begin the discussion with the thought that if we found a route which passes through every area then we would certainly get the maximum possible score. It would therefore be profitable to know whether such a route is possible or not. We will assume that such a route is possible and will use this assumption to lead either to the correct route or routes, or to a logical contradiction, thus proving that an all inclusive route is impossible. The maze puzzle in Figure 1 will be used to demonstrate the simpler aspects of the method.