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use the digits 8,6,1 &4 once each.Arrange the digits to make a 4- digit number.How many different 4-digit numbers can you make that are divisible by 7 with no remainder ?

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    I don't see a short-cut. Could this just be division practice?

    I make it two such numbers of 24 possibilities, one of which is 4186, and the other is predictable from that because 8 mod 7 = 1, and the equation (1000a + 100b + 10c + d = 0 mod 7) works out to (6a + 2b + 3c + d = 0 mod 7). But I still don't quite understand the intent behind the question. Maybe I'm missing something.

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