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Mehmet Guzey,

"I am trying to figure out how you determined the date (16 December 2020) just by using the Saturn-Jupiter distance and Saturn-Lunar distance. As far as i know, Saturn-Jupiter distances are equal almost every 20 years, so there are a bunch of suitable years from 2020 to 1900 for instance."

Well, even if we assume that the photo was not taken in recent years, we can still determine the exact date because the planets and the Moon never quite repeat their motions exactly. And we do not even have to assume that we can identify those planets as Jupiter and Saturn. Maybe they are Venus and Jupiter. But the fainter background stars guarantee only one solution to the puzzle in the past hundred years. The Moon and two bright planets have been close together like that and in those approximate locations on the border between Capricornus and Sagittarius only rarely (if at all) in the past few centuries. And they have been at those exact locations, among those background stars, only once in the past few centuries. It's a lock. If you didn't see it, go back and look at the original photo I posted in this thread with a bunch of fainter stars highlighted. Those guarantee the location in the sky. There is no other option. And from their positions, we know where those bright planets are in terms of RA (or SHA) and Dec down to a fraction of a degree. Adding the crescent moon in also gives us an approximate elongation from the Sun. All of this adds up to one and only one possibility taken at some specific time and fixed to small region on the globe. Before we add the lighthouse into the mix, it's interesting to consider what sort of error bars we can put on the time and location. 

Of course the "real" way that we know it was 2020 and not 1921 or 1941 is because iPhones were hard to come by back then (unless you could capture a time traveller!). Is that information allowed?? Does that make it cheating? Maybe... It all depends on how you choose to play the game. What can we accept as "givens" from the verbal setup of the story before we dig into the astronomical and mathematical implications? It's fair to assume that a recent photo is a "recent photo" in this context unless you have some reason to question that assumption. It is at least a good place to begin. If we play the game in a more pure form and assume nothing about the photo, then as I say above, it is still solvable thanks to those faint stars and thanks to the fact that the Solar System never really repeats.

Frank Reed