Ah, so G is the J of the non-duplicative world!
BirdsGalore.hs makes this nice and simple:
Problem 1: X3 (X1 X2) = G I
Problem 2: T = G I I
Problem 3: C = G G I I
Problem 4: R = C C
Problem 4: Q = G R (G I)
Problem 4: B = C Q
G again has a nice, fun behaviour, like J does.