I have -before- found the MLE of the two parameters of a Normal Distribution but I don't have any idea about how to proceed in this case. 

**Problem**

> 
> A sample of size $n$ is drawn from each of four normal populations, all of which have the same variance $\sigma^2$. The means of the four populations are $a + b + c$, $a + b - c$, $a - b + c$, and $a - b - c$. 
> 
> 
> What are the maximum-likelihood estimators
>  of $a, b, c$, and $\sigma^2$? 
> 
> 
> (The sample observations may be denoted by $X\_{ij}$, $i = 1,
> 2, 3,4$ and $j = 1,2, ... , n$.)
> 
> 
>