Definition:Hex (Game)

Definition

Hex is a two-person zero-sum game.

Board

The $n \times n$ Hex board is a particular arrangement of $n^2$ regular hexagons.

Specifically, they are centered on the lattice points in $\hointr 0 n \times \hointr 0 n$ of an oblique coordinate system.

The following is an example of an $11 \times 11$ board:

Tile

The regular hexagons which make up the Hex board are called tiles.

Adjacent

Two tiles on a Hex board are called adjacent if and only if they share an edge.

Sides

The extremities of an $n \times n$ Hex board, consisting of the edges of the $n$ tiles at its boundary, is a side of the board.

These sides are marked with $2$ distinctive colors such that opposite sides are the same color.

In the above diagram, the sides are $\color { red } {\text {red} }$ and $\color { blue } {\text {blue} }$.

Player

The two players in a game of Hex are identified by a symbol.

These symbols are conventionally modelled using counters of two contrasting colours, usually to match the colours of the sides of the board.

Those sides are identified with that player, who may be said to own those sides.

Moves

Each hex player takes turns.

Each player in turn selects a single unmarked tile on the board, and marks it with that player's symbol.

The players alternate turns until one or the other player wins.

Winning

A player wins if and only if there is a sequence of tiles $\sequence {h_i}_{1 \mathop \le i \mathop \le n}$ such that:

$(1): \quad$ Every $h_i$ is marked with that player's symbol

$(2): \quad h_i$ is adjacent to $h_{i + 1}$ for every $1 \le i < n$

$(3): \quad h_1$ is on one of the player's sides, and $h_n$ is on the other.

The player who has achieved that aim is called the winner.

Also see

• Results about Hex can be found here.