Water, light and gas

At first glance, the “Water, Light, and Gas” (or “Three Utilities Problem”) seems like a simple puzzle. It’s a challenge that invites us to connect three houses to the water, light, and gas supply centers, all without crossing the lines that represent the connections. However, behind this apparent simplicity lies an intriguing mathematical puzzle that delves into the depths of two fundamental areas of Mathematics: Topology and Graph Theory.

The goal is seemingly clear: the houses need to receive these three vital utilities, but the lines representing these connections cannot cross, creating a challenge that tests not only our spatial intuition but also our ability to think abstractly and logically.

Rules:

• Each house must be connected to the three utility centers (water, light, and gas), and each utility center must be connected to three different houses;
• The lines connecting the houses to the centers cannot cross at any point, ensuring that there are no intersections between them;
• The lines cannot pass directly through the utility centers (the water, light, and gas points). They must go around these centers, but cannot pass through them.

These rules are essential for solving the problem. Solving this puzzle involves the application of mathematical concepts, especially from Topology and Graph Theory, to create connections that meet all the established conditions.