Question

What is the smallest 3-digit number of the form aaa such that it is divisible by 9? (Here, a represents a digit.)

Answer 1

If all three digits need to be the same (I assume that's what aaa means) it's 333

Explanation:

For a number XYZ to be divisible by 9, X+Y+Z must be divisible by 9. Here's why:

X*100 + Y * 10 + Z = X + Y + Z + 99*X + 9*Y = X + Y + Z + 9(11X + Y)

So we need to find the smallest a so that a+a+a = 3a is divisible by 9. The smallest would be 0, but 000 is not a real 3-digit number. The next one is 3.