How many combinations of 16 characters can i have with 12 places? Repetition is allowed.

Question

The game no man's sky has a coordinate system using "glyphs", unique characters, of which there are 16, but the actual coordinates only use 12 of these 16 glyphs.

Repetition of glyphs are allowed. At a glance, i realize that this is an astronomically large number of unique combinations that are possible, but my question is what's the way to do the actual calculation? I'm not good at math and i feel like i should know this, but its not coming to me.

Answer 1

Hi Siddhant G.,

Assuming I read your problem statement correctly, you have 16 characters, in 12 dimensions, and you are drawing 12 times, with replacement. But there's an issue immediately: coordinate systems are not combinations, but rather permutations: 30N 60W is not the same place as 30W 60N!

So I'm guessing you really want permutations with replacement = 16^12 .

if you wanted combinations of those results anyway, that would get messy, as you would have to track instances of multiple draws of the same character, or of more than one character, etc. You might be able to come in on it as a probability thing, i.e. what is the probability of NOT having various multiple draws, similar to "same birthdays in the classroom" problems.

--Cheers, --Mr. d.