Problem:
A five-digit palindrome is a positive integer with respective digits , where is not zero. Let be the sum of all five-digit palindromes. What is the sum of the digits of ?
Answer Choices:
A.
B.
C.
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E.
Solution:
Note that . Because , the sum of all integers of the form is 450045 . For each value of there are choices for and . Similarly, the sum of all integers of the form is 45450 . For each value of there are choices for and . The sum of all integers of the form is 4500 , and for each there are choices for and . Thus . The sum of the digits is .
The problems on this page are the property of the MAA's American Mathematics Competitions