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Spring 2009 Week 1

1.    Consider an automobile odometer with 6 spaces, so that the number of miles showing can range from a minimum of 000000 to a maximum of 999999.  How many palindromes (i.e. numbers that read the same forwards and backwards, e.g. 274472) are there falling in this range?

2.    In general, how many palindromes can be created with n spaces being filled by r objects?  (Note for the odometer problem we have n = 6 and r = 10.)