How many palindromic numbers are there between ten and hundred thousand?

Answer 1

1089.

Explanation

A two digit palindrome will have the form AA, with A a digit between 1 and 9 (if A were zero, then this would not be a two digit number). So there are 9 possibilities for A and nine two-digit palindromes.

A three digit palindrome will have the form ABA, with A a digit between 1 and 9 (if A were 0, this would not be a three digit number) and B a digit between 0 and 9. So there are 9 possibilities for A and 10 for B. There are thus 9*10=90 three digit palindromes.

A four digit palindrome will have the form ABBA, with A a digit between 1 and 9 (if A were 0, this would not be a three digit number) and B a digit between 0 and 9. So there are 9 possibilities for A and 10 for B. There are thus 9*10=90 four digit palindromes.

A five digit palindrome will have the form ABBBA, with A a digit between 1 and 9 (if A were 0, this would not be a three digit number) and B and C each a digit between 0 and 9. So there are 9 possibilities for A, 10 for B, and 10 for C. There are thus 9*10*10=900 five digit palindromes.

Adding the above, we get a total of 9+90+90+900=1089 palindromes in the range.