Google Snacks Puzzle

Google placed this ad in the August 2004 issue of Dr. Dobbs. Is the puzzle easily solved with paper and pencil? Is it worth writing a program to solve the puzzle?

Would randomly picking 5 buttons over and over ever reach an answer?

Is that kind of knuckle-dragging, brute force problem solving ever justified?

Would you want to test all permutations of all combinations of 18 buttons taken 5 at a time?