# solving algebraic puzzle using the mathematica

I have tried to solve this algebraic puzzle,

$$abc+abc+abc=ccc$$

using mathematics but I don’t know what I am doing wrong. Can you help me?

I have tried these three ways

$$Reduce[3 (100 a + 10 b + c) == 100 c + 10 c + c, 0 <= a <= 9, 0 <= b <= 9, 0 <= c <= 9, Integers]$$

$$Solve[3 (100 a + 10 b + c) == 100 c + 10 c + c, 0 <= a <= 9, 0 <= b <= 9, 0 <= c <= 9, Integers]$$

$$FindIntance[3 (100 a + 10 b + c) == 100 c + 10 c + c, 0 <= a <= 9, 0 <= b <= 9, 0 <= c <= 9, Integers]$$