Unfortunately, I didn't see this puzzle until this week. And, I also didn't figure out the trick on my own. However, I wrote a program to generate all words of length $n$ using only the $m$'th letter(out of three) on a rotary telephone. This looks like this:

sh generate list 3 9 listOfWords

which would scan the list of words for length 9 words that only use the letters "a","d","g","j","m","p","t", and "w". It returns these as a list.

A fun thing to do(IMO) would be to learn some of these and write poems or stories with them.

Modern telephones have "q" and "z" where-as the older phones did not. To accomidate this modification, I wrote another script which is in a subdirectory. The main change is that you can request m=4 now(which only returns two values "s" and "z"), and your other lists for m=2 and m=3 change.

For the rotary telephones

First letters: "adgjmptw"
Second letters: "behknrux"
Third letters: "cfilosvy"

For the modern telephones

First letters: "adgjmptw"
Second letters: "behknqux"
Third letters: "cfilorvy"
Fourth letters: "sz"