+407 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?
+118667 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.
