A palindrome is a number that is identical when written both forwards and backwards. For example, 181, 25852, and 3333 are all palindromes. How many palindromes between 100 and 1000 are divisible by 3?

30 palindromes

Step-by-step explanation:

30

Step-by-step explanation:

zero cannot be the first digit of the palindromes. There are nine other numbers that can be.

9 * 10

The last digit also cannot be zero so it has the same value as the first digit. (Otherwise the number cannot be palindromic) So you are really looking at only 90 numbers total.

That's not the question, but it does put a limit on how many there can be.

Let's find the first number (closest to 100 ) that is palindromic and divisible by 3.

I think 111 is the smallest.

Now what about the largest? That would be 999.

So what is the next number after 111? Wouldn't that be 141?

The difference between 111 and 141 is 30

It turns out that any first digit that is divisible by 3, has 4 palindromic numbers because for them, the second digit is a 0. So for 3 for example, you get

303

333

363

393

All the other numbers only have 3 entries for example, 1 gives you

111

141

171

So making a table we get

First digit                          Number of palindromes divisible by 3

1                                        3

2                                       3

3                                                   4

4                                       3

5                                       3

6                                                   4

7                                       3

8                                       3                                            

9                                                   4

                                       18         12

Total