In how many ways can you group $3$ different numbers from $1$ to $12$ wherein their sum is divisible by $3$?
This question is one of the questions asked in a Math contest for intermediate level, particularly for grade 5 pupils. I know the answer but I do not know how it was solved. I also have tried the counting method but have counted 44 combinations only. Also tried elimination but stuck with 164 combinations, don't know what combinations to subtract from $12C3$. The answer to the question is $76$. Help please?