How many five-digit palindromes are there?
900 since the first three numbers are the only ones that matter there are 9*10*10 options
If you start to construct a five digit palindrome then the first digit can be any digit from 1 to 9. That is, there are nine choices for the first digit, which must then also be the fifth digit.
For the second digit you can choose any digit from 0 to 9 so there are ten choices for the second digit. This digit must also be placed in the fourth position if the number is to be a palindrome.
By the same reasoning there are ten choices for the third digit and this completes the number. Thus there are 9 x 10 x 10 = 900 choices for the first three digits and hence 900 five digit palindromes greater than or equal to 10,000.
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