How many palindromes between 1000 and 3000?

Answer 1

A palindrome reads the same forwards as backwards.

Therefore the first and last digits must be the same, the second and penultimate the same, and so on.

As 1000 & 3000 both have 4 digits, there are two pairs of digits that must be the same: the first and fourth, the second and third.

The first digit (and hence last digit) can only be 1 or 2 - a choice of 2

The second digit (and hence third digit) can be any of 0, 1, 2, ..., 9 - a choice of 10 for each of the choices of the first/last digit.

Thus there are 2 × 10 = 20 palindromes between 1000 and 3000.

Answer 2

1200

Answer 3

88