A positive integer whose digits are the same when read forwards or backwards is called a palindrome. For example 474 and 222 are palindromes. How many palindromes are there between 100 and 1000 ?
(A) 10
(B) 90
(C) 100
(D) 900
(E) 1000
Solution 1

The are 10 palindromes between 100 and 200: 101,111,121,131,141,151,161,171,181, and 191 .

The are 10 palindromes between 200 and 300: 202, 212,222, 232, 242,252, 262, 272, 282, and 292 .

Similary, there are 10 palindromes between each of 300 and 400,400 and 500, 500 and 600,600 and 700,700 and 800,800 and 900,900 and 1000 .

That is, there are 10 palindromes between each of the 9 pairs of consecutive multiples of 100 from 100 to 1000 .

The number of palindromes between 100 and 1000 is $10 \times 9=90$.

## Solution 2

Each palindrome between 100 and 1000 is a 3-digit number of the form $a b a$, where $a$ is a digit from 1 to 9 inclusive and $b$ is a digit from 0 to 9 inclusive, and $a$ and $b$ are not necessarily different digits.

Thus, there are 9 choices for the first digit $a$ and each of those choices determines the third digit which must also be $a$.

There are 10 choices for the second digit $b$, and so there are $9 \times 10=90$ choices for $a$ and $b$.

Thus, there are 90 palindromes between 100 and 1000 .

ANSWER: (B)