TITLE: Determine date of birth from "astrological" signs?
QUESTION [7 upvotes]: Suppose someone tells me what constellation the Sun, Moon, Mercury,
Venus, Mars, Jupiter, and Saturn were in when they were born, and the
information is astronomically accurate (ie, not astrological signs).
Could I use this information to estimate their date of birth
(including year) to a reasonable approximation? My thoughts:

12 constellations, 7 planets (incl Sun/Moon) yields 35,831,808
possibilities, and we know the moon changes constellations daily. If
the planets were in purely random constellations every day, it would
take 98104 years for all possible combinations. Using this, and
additional information that the person was born in the last 200
years, it would seem easy to find their birth date.
Of course, planets aren't in random constellations. Additionally, 
the birthday paradox suggests there will be many repeats despite the 
35,831,808 combinations. 

However, it still seems like you could do a fairly good job of 
approximating someone's birthday with this information?

REPLY [2 votes]: You could not calculate the exact date of birth because the Moon is in the same constellation for up to 3 consecutive days, and the other bodies for much longer.  
The second problem is that constellations of Mercury and Venus are not independent of the constellation of the Sun.  Mercury will usually be in the same constellation as the Sun (maximum elongation 28 degrees).  
Additionally, the constellations are defined to be different sizes and the Sun can stay in the same constellation for up to 45 day.  You could have a situation where the Moon makes a complete orbit of the Earth while the other bodies haven't changed constellation.
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