Graph Coloring and Cycles

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Short Circuit; or Graph Coloring and Cycles

Components

Game Board

Connectors, two colors for each player (four total colors)

Capacitors

Overview

The goal of the game is to arrange your connectors on the board in such a way that creates a closed circuit. Players alternate taking turns of playing one piece at a time and sometimes blowing up capacitors. Whoever creates a closed circuit first wins.

Setup

The starting player is the player who last used a desktop computer.

The player who will play second puts one of their connectors in the center of the board. Then, the starting player puts a connector adjacent to that piece in the middle. After that, play begins with the starting player.

Gameplay

The turn structure is as follows: pop any number of capacitors, then, play one piece.

Each turn, a given player will play one piece, choosing from either color of their connectors or a capacitor. Each spot on the board can hold one connector and one capacitor. When you play a connector, you must play it adjacent to one of your connectors of a different color. However, you may not play a connector adjacent to a connector of the same color. Because of this rule, you have to plan ahead so that you don’t prevent yourself from playing on a certain space.

Playing the capacitor doesn’t have as much restriction on where you can play it. You may play a capacitor on or adjacent to one of your connectors.

But before you play a piece, you may pop any number of capacitors. To pop a capacitor, you must have one of your connectors on or adjacent to a capacitor, and that connector must have another connector of any color adjacent to it. When you pop a capacitor, remove that capacitor from the board, as well as the connector mentioned second (the one not necessarily next to the capacitor).

After popping a capacitor on your turn, you may not play a capacitor that turn.

Win Condition

At the end of a player’s turn, if they have played connectors such that they form a loop (or a closed circuit), that player wins. The smallest possible loop is made of six connectors forming a hexagon.