2020/21 AHSMC Part 1 Problem 5

Problem 5 of 16

A number which reads the same backwards as forwards is called a palindrome. For example, $13231$ is a palindrome, since backwards it also reads $13231$ . How many palindromes are between $10$ and $2020$ ?

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There are $9$ two digit palindromes ( $11$ , $22$ , $\ldots$ , $99$ ) and $90$ three digit palindromes (all numbers of the form $aba$ , where $a$ and $b$ are digits and $a \neq 0$ ). Any four digit palindrome smaller than $2020$ must have the form $1aa1$ or $2002$ , hence there are $11$ such palindromes. Therefore the number of required palindromes is $9+90+11=110$ . The answer is (D).

University of Alberta

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