Originally posted by: sirjonk
Cheated
http://www.gamebanshee.com/sta.../locations/dunesea.php
The solution is abstractly obvious yet makes perfect sense. It's ingenious:
The progression goes like this:
4,
14,
11-14
31-14
13-21-14
From this you get, 31-13-12-14 , 23-41-12-14.
The solution in each step is that you describe how many there are of each digit in the previous answer. So begin with 4 (could be anything here but that's what they started with). You have just one four. That's expressed simply as "14," because you have one four, hence the next answer. Now describe each digit in "14." You have just one 1, and one 4. So that's expressed as "11-14." Now describe that. You now have three 1's, and still just one four. So the answer is "31-14." Now describe that (in order of appearance by the way). You have one 3, two 1's and one 4 in that expression, which makes the answer "13-21-14." Finally, describe that and the next one, in order of appearance. You have three 1's, one 3, one 2, and one 4, equaling "31-13-12-14" and following that, two 3's, four 1's, one 2, and one 4, equaling "23-41-12-14," your answer.
If we were to extend it one further we'd have two 2's, one 3, two 4's, and three 1's, making "22-13-24-31." Got it? Hope so.