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Washington and Lee University

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March Problems

Easier Problem: 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?

Harder Problem: 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.)