Math

Most films these days are distributed with “extras”, usually including a short feature (of limited interest) whose title begins “The Making of …”. This page is an “extra” for SpellCubed”—“The Making of SpellCubed”.

The construction of SpellCubed involves mathematics: geometry, combinatorics, probability and set theory, The player does not have to be aware of any of this.

The connection to geometry is through geometric symmetry. Fundamental to the game are the rotational symmetries of a cube. It is easy to see that one can rotate a cube to 24 positions.

Combinatorics enters when we try to count or even estimate the number of certain possibilities. For example the number of arrangements of n different items in a row is n!. In particular in SpellCubed there are 24=4! ways of arranging four different cubes in a row and 125=5! ways of arranging five different cubes in a row.

Many of the methods of SpellCubed involve “random” choice and this is a concept from probability.

Underlying some of the ideas of SpellCubed are from theory of sets. A basic notion in set theory is that of an equivalence relation. One can summarize the discussion of Spells and Symmetry (click to get to that page if you want) by saying that a Spell is really an equivalence class of the sequences of four words.