SOLUTION: Arranging digits. In how many ways can you arrange the digits 8,7,6 and 3 to form a four-digit number divisible by 9, using each digit once and only once?

Question 217790: Arranging digits. In how many ways can you arrange the digits 8,7,6 and 3 to form a four-digit number divisible by 9, using each digit once and only once?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Arranging digits. In how many ways can you arrange the digits 8,7,6 and 3 to form a four-digit number divisible by 9, using each digit once and only once?
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I don't think any of the arrangements are divisible by 9.
Numbers divisible by 9 have this property that the sum
of the sum of the sum of the digits is divisible by 9.
For example the sum of 27 = 9 so 27 is divisible by 9.
But the sum of your digits is 24 = 6, so, as an example,
6783 would not be divisible by 9; and it is not.
Cheers,
Stan H.
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