You should understand that there are infinite solutions to such questions, and #19 can well declare what you give is not what he has in mind.
Patterns, as we see them, from as small as a sequence of numbers to as big as the evolution of everything in the universe, can all be explained with infinitely many equally valid governing rules or laws. For the explorer, the only thing he can claim is that the rule he has discovered is CONSISTENT with the observed part of the pattern. He can never prove it is actually THE governing law.