Definition:Magic Hexagon

Definition

A magic hexagon is a centered hexagonal pattern of cells containing the natural numbers from $1$ to the number of cells such that the numbers in all the cells in a given straight line all add up to the same number.

Line

A line of a magic hexagon is a set of consecutively adjacent cells, in any of the three directions parallel to the sides of the underlying hexagon.

Order of Magic Hexagon

Let $H$ be an magic hexagon created on the $n$th centered hexagonal number.

That is, let $H$ have $n$ cells along each side.

Then $H$ is an order $n$ magic hexagon.

Magic Constant

The magic constant of a magic hexagon is the number that each of the lines adds up to.

Examples

Order $1$

Order $3$

Also see

• Results about magic hexagons can be found here.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $19$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $19$

• Weisstein, Eric W. "Magic Hexagon." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MagicHexagon.html