= Solution
{c}
For an $n$-vertex <fermion loop>, reversing the <fermion flow> reverses the ordered product inside its <trace>. The same <charge-conjugation matrix> calculation transforms every <Dirac propagator> by $p\mapsto-p$ and contributes $-1$ for each vector photon <interaction vertex>. Relabel the <loop momentum> so that the external labels are fixed. The reversed <Feynman diagram> therefore obeys
$$
\boxed{\mathcal M_{\rm reversed}=(-1)^n\mathcal M_{\rm original}.}
$$
For odd $n\geq3$, the $(n-1)!$ cyclic orders pair into opposite orientations and cancel. For $n=1$, the single photon tadpole maps into itself with a minus sign and is zero. The common <closed fermion loop sign> is present on both sides and does not supply the factor $(-1)^n$. This proves <Furry's theorem> for all the requested <one-loop Feynman diagrams>. The <charge conjugation> argument also gives vanishing odd-photon <correlation functions> to all orders in vacuum <QED>, provided no <charge conjugation symmetry> breaking background or charged external state is introduced.
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