= Solution
The five-membered enone-like <carbon> framework can be obtained by an intramolecular <aldol condensation> of
$$
\mathrm{MeCOCH_2CH(CN)CH(CN)CH_2COMe}.
$$
Enolization at an internal methylene next to one <ketone> followed by attack on the opposite <ketone> closes a five-membered ring. <dehydration> leaves one acetyl group attached to one <alkene> <carbon> and one methyl group on the other. The two nitrile-bearing <carbons> remain adjacent and their original cis relationship is retained if <epimerization> is avoided.
Now reverse a reductive <ozonolysis>: the diketone arises by opening a six-membered <cyclohexene> whose <alkene> <carbons> each carry Me. That <cyclohexene> is the <Diels-Alder reaction> product of \b[2,3-dimethylbuta-1,3-diene and <maleonitrile>]. The latter is the supplied cis dinitrile. The <stereospecificity> of the cycloaddition puts the two CN groups on the same face.
Thus the forward plan is \b[Diels–Alder addition, reductive <ozonolysis>, then five-membered aldol ring closure and <dehydration>]. Use a reductive ozone work-up that stops at the diketone. During the final step, avoid prolonged strongly basic heating because the <carbons> bearing CN can be deprotonated and epimerized. Achiral reagents give the racemic pair with the required cis relationship; resolution would be necessary if only the depicted <enantiomer> were required. The diene supplies six <carbons> and <maleonitrile> supplies four, accounting for all ten <carbons> without an unexplained <carbon> deletion.
\Image[/past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-1-ring-transformations.png]
{title=Atom tracing through the two cycloaddition and ring-reorganization routes}
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