---
tag: M9Y2A9JJPE
kind: problem
name: Three utilities problem
aliases: [3-cottage-problem, 3-cottages-problem, 3-utilities-problem, 3-utility-problem, electricity-gas-and-water, electricity-gas-water, electricity-water-and-gas, electricity-water-gas, gas-electricity-and-water, gas-electricity-water, gas-water-and-electricity, gas-water-electricity, impossible-house-puzzle, supuzzle, thomsen-graph, three-cottage-problem, three-cottages-problem, three-utility-problem, utilities-problem, utility-graph, water-electricity-and-gas, water-electricity-gas, water-gas-and-electricity, water-gas-electricity]
sources:
  - wikipedia: en:58862@r1337576115
    locator: Three utilities problem
    note: adopted
    mention: wikipedia://en/58862
    sections: [Problem]
same_as:
  wikidata: Q32918
  wikipedia: Three utilities problem
inventory: [QZT9WBH6G6]
---

## Problem

The **three utilities problem**, also known as **water, gas and electricity**, is a mathematical puzzle that asks for non-crossing connections to be drawn between three houses and three utility companies on a plane. When posing it in the early 20th century, Henry Dudeney wrote that it was already an old problem. It is an impossible puzzle: it is not possible to connect all nine lines without any of them crossing. Versions of the problem on nonplanar surfaces such as a [[torus|03NM7DZXXC]] or [[Möbius strip|04AJE0M271]], or that allow connections to pass through other houses or utilities, can be solved.