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

To find the number of palindromes between 1000 and 3000, we can break it down by the possible combinations of digits. There are 10 choices for the first digit (1-2), 10 choices for the second digit (0-9), and only 1 choice for the third digit (the same as the first). Therefore, there are 10 * 10 * 1 = 100 palindromes between 1000 and 3000.

Answer 3

Oh, what a delightful question! Let's take a moment to appreciate the beauty of palindromes. Between 1000 and 3000, there are 109 palindromic numbers, each one a little work of art in its symmetry. Keep exploring the wonders of numbers, my friend, and let your creativity flow like a river of paint on a canvas.

Answer 4

There are 109 palindromes between 1000 and 3000. But seriously, who has time to count all those palindromic numbers? Just trust me on this one, honey.

Answer 5

1200

Answer 6

88