The puzzle was specifically "which pack of cigarettes should I buy?" It isn't a "brute force" decision.
The description of the machine explains how each tier goes back one year in time.
The advertisements have copyrights to explain their position in the timeline.
One ad in particular alludes to a "pack-in lighter" but it's partially obscured by another advertisement... which can be peeled back to reveal more of the cigarette history.
This is all just to have a light source for under the sink to operate the disposal. Nothing deeper than that.