Q: A palindromic number is like a palindrome word (like “kayak”) which reads the same forwards and backwards. Find all the 3 digit palindromic numbers that are multiples of 18 (see if you can find a clever way of doing this).

A: There are 4 numbers that meet this criteria: 252, 414, 666, 828

Any and all multiples of 18 have to be multiples of 9 and also have to be even so the number must end with a 2, 4, 6 or 8 which means that it must also begin with a 2, 4, 6 or 8 as the number is palindromic.

Looking at 3 digit numbers that begin and end with 2 whose digits add up to 9 or a multiple of 9 only yields 252.

Looking at 3 digit numbers that begin and end with 4 whose digits add up to 9 or a multiple of 9 only yields 414.

Looking at 3 digit numbers that begin and end with 4 whose digits add up to 9 or a multiple of 9 only yields 414.

Looking at 3 digit numbers that begin and end with 6 whose digits add up to 9 or a multiple of 9 only yields 666.

Looking at 3 digit numbers that begin and end with 4 whose digits add up to 9 or a multiple of 9 only yields 828.