How many palindromic numbers in 1-10000?

Answer 1

10001

Answer 2

• In the range 1-9 there are 9 - all the single digit numbers
• In the range 10-99 there are 9 - all the double digit numbers (11, 22, etc)
• In the range 100-999 there are 90 - the first and last digits must be the same (there are 9 of these: 1-9 as the first digit cannot be 0) and the middle digit can range over all the 10 digits 0-9, making 9 × 10 = 90
• In the range 1000-9999 there are 90 - the first and last digits must be the same (there are 9 of these: 1-9 as the first digit cannot be 0), and the middle two digits must be the same and can range over all the 10 digits 0-9 making 9 × 10 = 90
• The last number 10000 is not palindromic.

In total there are 9 + 9 + 90 + 90 = 198 such numbers.

Answer 3

There are 198 such numbers.