= Solution
The light <pseudoscalar meson nonet> has $J^P=0^-$ and flavor structure $3\otimes\bar3=8\oplus1$. Its members are the three <pions>, four <kaons>, and the two neutral isospin-zero states <eta meson> and <eta prime meson>. For mesons the <baryon number> is zero, so the <Gell-Mann--Nishijima formula> reduces to
$$
\boxed{Q=I_3+S/2.}
$$
Here $S$ is <strangeness>, with an $s$ <quark> carrying $-1$ and an <antiquark> $\bar s$ carrying $+1$. Thus the upper row is $K^0=d\bar s$ at $(I_3,S)=(-1/2,1)$ and $K^+=u\bar s$ at $(1/2,1)$. The lower row is $K^-=s\bar u$ at $(-1/2,-1)$ and $\bar K^0=s\bar d$ at $(1/2,-1)$. The charged <pions> lie at $(\pm1,0)$, while $\pi^0,\eta,\eta'$ share $(0,0)$ as flavor-weight coordinates.
The neutral <pion> direction is $(u\bar u-d\bar d)/\sqrt2$. The octet and singlet isoscalar directions mix to make the physical eta and eta-prime states; counting three central states is essential to obtaining nine rather than seven particles. Horizontal lines in the diagram have constant $S$, while lines $I_3+S/2=Q$ mark constant charge. Meson exchange describes part of the residual nuclear force; the underlying quark-level <strong interaction> is mediated by <gluons>, not by treating <pions> as elementary gauge bosons.
\Image[/past-exam-of-the-sub-atomic-physics-course-of-the-university-of-oxford/2016-pseudoscalar-meson-nonet.png]
{title=Light pseudoscalar meson nonet with charge and strangeness lines}
{description=Original flavor-weight diagram. Three neutral states share the central weight; diagonal guides show constant charge and horizontal guides constant strangeness.}
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