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Erica and Andrew are playing a game. Erica starts by selecting three digits a, b, and c, and then Andrew needs to select a digit x such that the six-digit number $$\overline{axbxcx}$$ is a multiple of 9. What is the sum of all possible values of $$a + b + c$$ that would give Andrew exactly 3 choices of x?

Oct 18, 2020

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This is a weird question.

If a+b+c  = 6 or 15 or 24     then    x could be equal to 1 or 4 or 7

If a+b+c  = 3 or 12 or 21    then     x could be equal to  2 or 5 or 8

If a+b+c = 0 or 9 or 18 or 27 then  x could be equal to  0,3,6 or 9     There are 4 of them so that is no good.

So 3 possible values of x will happen when

a+b+c = 3,6,  12 15,  21,24

Now you can finish it.

Oct 18, 2020