Problem#14
A five-digit palindrome is a positive integer with respective digits where is non-zero. Let be the sum of all five-digit palindromes. What is the sum of the digits of ?
This problem is a part of the series <One minute problems>
The answer is 18.
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1 solution
The smallest five digit palindrome number is 10001 and the biggest is 99999 Adding then 10001+99999=11000 There are 9 × 1 0 × 1 0 × = 9 0 0 or 450 pairs of panildromes which sum to 11000. Multiplying 4 5 0 × 1 1 0 0 0 = 4 9 5 0 0 0 0 Adding 4 + 9 + 5 = 1 8 So the sum will be 18