What is the smallest five-digit plaindrome that is divisble by $11$?
My first thought was $10001$ is this right?
+128460 10001 isn't divisible by 11
If we assign alternating signs to successive digits and the sum of the digits = 0 (or 11), our number is divisible by 11
For example
121 = +1 - 2 + 1 = 0 = divisible by 11
506 = +5 - 0 + 6 = 11 = divisible by 11
The smallest I can find is
10901 = +1 - 0 + 9 - 0 + 1 = 11 = divisible by 11
