Here are a bunch of equations to "solve":
b + c = 1
a + b + c = 7
b + c + f + g = 4
a + b + c + d + g = 3
a + b + e + d + g = 2
Of course, this is an underdetermined system, so if you think you have the answer, in order not to spoil it for others just reply with a new equation these variables satisfy - there are several more of them.
In approaching this problem my only suggestion is to not be led astray by conventional thinking. To solve the puzzle you'll have to display some ingenuity and out-of-the box thinking. I'm sure the answer will be more obvious to some segments of EE community than others but everyone regardless of their background should be able to get it.