I just want to comment on something, at first glance all the solutions posted on this page look kind of complicated for such a simple thing. But you almost never need to write such code in the real world.
In actual apps, you want to iterate over some collection of data items. The for
or while
loop is how you do that in an imperative language: you have some “iterator” kind of value–a simple index for an array, something else for a map or set–increment that, check if it’s out of range, use it to access your data collection.
In functional languages, you pass the operation you want to perform on the data as an argument to one of the collection’s functions. In Elixir, Enum.map
or Enum.reduce
. This actually results in more compact code because it eliminates the whole “get an iterator, increment, check it, use it” dance.
So while this particular exercise can help you understand some low-level mechanics of Elixir, it could also be misleading. Please don’t think you have to jump through the hoops of all these solutions in order to do something with an array of values you get back from your database or submitted from a web form 
That said, here is my solution:
Enum.each(10..1, fn(i) -> IO.puts(i) end)
or, using some shorthand:
Enum.each(10..1, &(IO.puts("#{&1}")))
or, if you want to prove you actually understand passing around functions:
Enum.each(10..1, &IO.puts/1)
But even that could be misleading, because in a functional language you don’t often just “run a loop” over a collection for side effects, you usually produce a value, either a set of values produce from each source value (Enum.map
) or a single value derived from the whole set (Enum.reduce
).