How many Spells?

{How many different Spells are there?

The short answer is “a lot”.
But it is very difficult to calculate.

Suppose we have a given Roll of FOUR CUBES and, to keep calculations simple suppose no Cube in the Roll has two of the same letter on any single cube.

There are 4!=24 different arrangements of these cubes in a row.

Coincidentally there are 24 different rotations of a cube.

That gives us $4! * 24 * 24 * 24* 24 =7,962,624$ arrangements of these cubes in a row.

According to the discussion in  Spells and Symmetry page this calculation should be divided by 8 and so we come up with 7,962,6248 = 995,328 . So “about a million”. Bottom line—you don’t want to resolve a Roll into a 4Spell by only trial and error!

But that is a million possibilities for ONE ROLL. And how many rolls? A Roll must have at least one Spell so must correspond to four different words. Our default Dictionary of Four Letter Words has about 2250 words. This means roughly 22504 possible spells or 25,628,906,250,000. Even accounting for the symmetries etc, there are trillions of possible 4 Cube Spells. Bottom line—that’s what is meant by “you will never run out of Spells in SpellCubed”. And of course if we use the alternate large four letter word list of 4446 words, we get even more—you do the math.

By the way there are about 5000 FIVE letter words in our default Dictionary and
50005 = 625,000,000,000,000$—over half a quadrillion! …And there are 9631 five letter words in the large list!