Hey folks, I really appreciate all the feedback.
I'm enjoying thinking about all the ideas offered. I don't think the solar option will work well, because as vne157 guessed, the container will be hidden and won't get much if any sunlight. I'm not really concerned about power capacity, because there will be lots of room available in the container and I'm happy just using a four pack of D cells for practically unlimited "on" time.
I am having to restrain myself from jumping on the more complex ideas because I don't want to frustrate people in the field. The point of the hobby is the hunt and if they are able to find the box, then I don't want them to be prevented from getting to the next stage because they can't figure out the settings. And sometimes they'll be standing in the rain, or it will be really hot, or they'll have small children with them, etc, so I want to make it more enjoyable/easy than satisfying-to-solve-but-hard. So it's a fine line I'm trying to walk--just hard enough so that's it's not a giveaway, but not too hard. Maybe a 2 or 3 on a scale of 10. So I guess I'm looking more for electronic "bells and whistles" than difficulty. I thought about have one extra display unit to show how many switches were set correctly at any given time, but then I realized that would be TOO easy--they would just have to cycle each switch and see if the count went up or down.
Maybe some kind of "victory dance" of leds surrounding the display when the solution is found? Maybe something that would play an audio clip (the theme of the cache is "Snoopy and the Red Baron--Snoopy has been shot down behind enemy lines and is being held hostage; the cacher has to get the coords of the military outpost and go rescue him--so it could play the "Snoopy vs. the Red Baron" song
), maybe the display could be sympathetic and flash the correct settings in binary after a certain number of failed attempts...?
But please keep all the ideas coming. I'm collecting them for future caches that I want to make intentionally hard