Find me plzzz...Number Theory Level 4
An 8-digit number has a property that the number formed by ANY permutation of it's digits is always divisible by 11. If I am given that the original number is divisible by 5 , what is the sum of digit sums of all the possible distinct numbers formed by permutations of digits of the 8-digit number ?
DETAILS and ASSUMPTIONS :-
Digit sum of number \(879489\) is \(8+7+9+4+8+9 = 45\)
\(00098765\) is a 5 digit number , not 8-digit.
ALL the possible numbers formed by permutations of digits of the number \(234\) are :- \(324,342,423,432 ,243,234\) (yeah , the number itself is also counted)