A sum of palindromes
Probability
Level
4
What is the sum of all 5-digit palindromes?
(Palindromes are the numbers which are read the same both forward and backward. For example, 343 and 7887 are palindromes, while 123 and 9988 are not.)
The answer is 49500000.
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1 solution
5-digit palindromes are in the format ABCBA, with A ranging from 1 to 9, and B and C ranging from 0 to 9.
Therefore, there are 9 * 10 * 10 = 900 five-digit palindromes.
The average "A" digit is 5, the average "B" digit is 4.5, and the average "C" digit is 4.5. This way, the "average 5-digit palindrome" is: 5 * 10000 + 4.5 * 1000 + 4.5 * 100 + 4.5 * 10 + 5 * 1 = 50000 + 4500 + 450 + 45 + 5 = 55000
Therefore, the sum of all 5-digit palindromes is 900 * 55000 = 49500000.