Licence plates
February 12, 2012
Oregon licence plates consist of three letters followed by a three digit number (each digit can be from [0..9]). While driving to work Seth plays the following game: Whenever the numbers of two licence plates seen on his trip add to 1000 that's a win.
E.g. MIC-012 and HAN-988 is a win and RYU-500 and SET-500 too. (as long as he sees them in the same trip).
Find the expected number of plates he needs to see for a win. Give your answer rounded to 8 decimal places behind the decimal point.
Note: We assume that each licence plate seen is equally likely to have any three digit number on it.
Written by gamwe6 who lives and works in San Francisco building useful things. You should follow him on Twitter