= Solution
{c}
Replace every coloured site in the drawing by an identical site carrying $\bar f$. The face-centering <lattice translations> now preserve the average <crystal structure>, whose <Bravais lattice> is a <face-centered cubic lattice>. One choice of <primitive lattice translation vectors> is
$$
\mathbf a_1=\frac a2(0,1,1),\qquad
\mathbf a_2=\frac a2(1,0,1),\qquad
\mathbf a_3=\frac a2(1,1,0).
$$
A coherent <Bragg diffraction> peak requires $\mathbf G\cdot\mathbf a_j\in2\pi\mathbb Z$ for all three <primitive lattice translation vectors>. Thus $k+l$, $h+l$, and $h+k$ must all be even, equivalent to all three <Miller indices> having the same <integer parity>. This is the <face-centred cubic selection rule>: $(110)$ is forbidden and $(111)$ is allowed. The restoration of these <lattice translations> explains the disappearance of the ordered <superlattice reflections>.
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