How to solve this context free grammar

Question

Give a Context free grammar for

{w | w is an element of {a, b, c, d}* such that # of a+ # of b = # of c + # of D}

how do i approach this question...?

Answer 1

How's about this one:

S -> A C S     
S -> A S C                   
S -> S A C                 

S -> C A S     
S -> C S A                   
S -> S C A

S -> 
A -> a|b
C -> c|d

(There may be a more elegant solution...)

As to how to approach these, in my opinion the key insight is usually in the grouping (here A and C), but the I think the best way to learn is to see lots of examples and attempt lots of problems - e.g. this one.