Question 1067319: How many 3 digit palindromes are divisible by 3? Thanks for any help .
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! While the middle digit could be any of the 10 digits, including 0,
he first and last digits cannot be zero.
They must be one of the  choices from 1 though 9.
So, there are  3-digit palindromes,
For a number to be divisible by 3 , the sum of the digits must be divisible by 3.
Of the 9 choices for first (and last) digit, 3 are multiples of 3,
another 3 have a remainder of 1 when divided by 3,
and the other 3 have a remainder of 2.
For any middle digit, there will be  out of the choices of first and last digits that will make the sum of digits a multiple of 3.
If the middle digit is has a remainder of 0 when divided by 3 (as happens for 0, 3, or 9),
a first/last digit that is a multiple of 3 makes the sum a multiple of 3.
If you the middle digit has a remainder of 1 when divided by 3,
a first/last digit with a reminder of 1,
will make the 3 remainders add up to 3,
for a sum that is a multiple of 3.
If you the middle digit has a remainder of 2 when divided by 3,
a first/last digit with a reminder of 2,
will make the 3 remainders add up to 6,
for a sum that is a multiple of 3.
Of the  palindromes,  or 
will be divisible by 3.
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