Art of Problem Solving

1991 AHSME Problems/Problem 17: Difference between revisions

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How many years in the millenium between 1000 and 2000 have properties (a) and (b)?
How many years in the millenium between 1000 and 2000 have properties (a) and (b)?
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Revision as of 12:53, 5 July 2013

A positive integer $N$ is a palindrome if the integer obtained by reversing the sequence of digits of $N$ is equal to $N$. The year 1991 is the only year in the current century with the following 2 properties:

(a) It is a palindrome

(b) It factors as a product of a 2-digit prime palindrome and a 3-digit prime palindrome.

How many years in the millenium between 1000 and 2000 have properties (a) and (b)? These problems are copyrighted © by the Mathematical Association of America.