A 3 digit palindrome is a 3 digit number (not starting with zero) which reads the same backwards as forwards For example, 242. The sum of all even 3 digit palindromes is `2^(n_(1))*3^(n_(2))*5^(n_(3))*7^(n_(4))*11^(n_(5))*` value of `n_(1)+n_(2)+n_(3)+n_(4)+n_(5)` is

Explanation

L:et number of the form palindrome be `alpha beta alpha`.
Now, If `alpha beta alpha` is even, then `alpha` may be `2,4,6,8` and `beta` take values `0,1,2,"……"9`.
So, total number of palindrime (even) `=10xx4=40`
To find the sum of all even 3 digit plaindrome
So, sum of number start with 2
`=(200+2)xx10+(0+1+2+3+"......"+9)xx10=2020+450=2470`
Sum of number srart with `4=(404)xx10+450`
Similarly, sum of number start with `6=(606)xx10+450`
Similarly, sum of number start with `8=(808)xx10+450`
`:.` Total sum `=(202+404+606+808)xx10+450xx4`
`=20200+1800=22000`
`=2^(4)xx5^(3)xx11`
On comparing `2^(4)xx5^(3)xx11^(1)` with
`2^(n_(1))xx3^(n_(2))xx5^(n_(3))xx7^(n_(4))xx11^(n_(5))`
`n_(1)=4,n_(2)=3,n_(3)=0,n_(4)0,n_(5)=1`
Now, `n_(1)+n_(2)+n_(3)+n_(4)+n_(5)=8`.