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**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)

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