= Solution
The supplied schematic has four daughter <energy levels>, including the <ground state>, and all six downward pair transitions. Thus the observed <gamma ray> <energies> must be the six positive pairwise differences of
$$
0<E_1<E_2<E_3.
$$
The largest difference fixes $E_3=2.982\,\mathrm{MeV}$. Since $E_1,E_2$ are themselves transitions to the <ground state>, each must occur among the measured <energies>. Testing those pairs gives exactly \b[two level schemes]:
$$
\boxed{\begin{aligned}
\mathrm A:\ &(E_1,E_2,E_3)=(0.440,2.076,2.982)\,\mathrm{MeV},\\
\mathrm B:\ &(E_1,E_2,E_3)=(0.906,2.542,2.982)\,\mathrm{MeV}.
\end{aligned}}
$$
They are reflections of one another about half the total span: replacing every level $E$ by $E_3-E$ preserves the set of differences. The assignment of every observed line is
$$
\begin{array}{c|cc}
\text{Transition}&\mathrm A&\mathrm B\\\hline
1\to0&\gamma_1&\gamma_2\\
2\to0&\gamma_4&\gamma_5\\
3\to0&\gamma_6&\gamma_6\\
2\to1&\gamma_3&\gamma_3\\
3\to1&\gamma_5&\gamma_4\\
3\to2&\gamma_2&\gamma_1
\end{array}
$$
\Image[/past-exam-of-the-particle-and-nuclear-physics-course-of-the-university-of-cambridge/2022-gamma-level-schemes.png]
{title=The two level schemes reconstructed from the six gamma-ray energies}
These original diagrams plot the inferred <excitation energies> to scale. They do not reproduce the source schematic. The reconstruction treats the supplied three-decimal <gamma ray> <energies> as the transition gaps, neglecting their much smaller <nuclear recoil> corrections.
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