# Problem 371: Licence plates 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.