## What is the utility problem in graph theory?

The utility problem posits three houses and three utility companies–say, gas, electric, and water–and asks if each utility can be connected to each house without having any of the gas/water/electric lines/pipes pass over any other.

**Can you connect the same letter dots without crossing the line?**

Lines must always join two different dots in the same hexagon, but they don’t need to be straight. To make it more of a challenge, no two lines can join the same pair of dots. And for the 3-line and 4-line challenges lines cannot cross. In the final puzzle below, each dot connects a different number of lines.

### Can you connect two houses to three utilities?

It’s not hard to see this is impossible. Connect two houses to the three utilities, and you will essentially have a square with one diagonal drawn. The two corners joined are two of the houses, the other two corners and the midpoint of the diagonal are the utilities.

**Is there a puzzle with 3 houses and 3 Utilities?**

There’s a puzzle where you have 3 houses and 3 utilities. You must draw lines so that each house is connected to all three utilities, but the lines cannot overlap. However, I’m fairly sure that the puzzle is impossible. How is this proved? It’s not hard to see this is impossible.

#### How many houses can you connect to gas and electric?

Classic puzzle about connecting three utilities, gas water and electric, to three houses, without crossing any of the lines. Connecting Gas Water & Electric to Three Houses. Answer to Puzzle #26: Gas, Water, Electric to 3 Houses

**How do you connect a utility to a house?**

Your job is to connect each utility to each home WITHOUT crossing any lines. You may not pass a line through a house or other utility circle. Leave an inch and a half between each house. Put each circle an inch below each square. So we have to draw nine (curved) lines, connecting each dot at the bottom to each of the houses.