<s>[INST] Three-Digit numbers divisbile by 3 How many three digit numbers are divisible by 3 and have an additional property that the sum of of their digits is 4 times the middle digit?
My approach: let the number be $abc$ so $$abc \equiv 0\pmod{3}$$ and $$a + b+ c= 4b$$
I'm stuck now. Any help?
 [/INST] First, $b$ should be dividable by $3$, since $a+c=3b$, we have $0<3b<18$. So $b$ can be $3$ and $6$.
For $b=3$, we have $a+c=9$, there are 9 choices;
for $b=6$, we have $a+c=18$, then the only choice is $a=c=9$.
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