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]$ $