= Solution
The left ring system is \b[spiro], and the right-hand substituent is \b[$\mathrm{CH(OMe)Me}$], not OMe directly attached to the <cyclohexene> ring. Let $Q$ denote the right cyclohexenyl group bearing that methoxyethyl substituent cis to its linker. The connection to the left alkene <carbon> is $\mathrm{-(CH_2)_3-Q}$. These observations suggest two Diels–Alder constructions. A left-hand <diene>
$$
\mathrm{(cyclopentane)C=C[(CH_2)_3Q]-CH=CH_2}
$$
has the original <cyclopentane> <carbon> as one terminal <diene> atom; cycloaddition with an <ethylene equivalent> gives the spiro six-membered ring. Its residual double bond is between the two internal <diene> atoms, putting the linker on the required alkene <carbon>.
Build $Q$ and its four-carbon <alcohol> appendage first. Protect the OH group of the indicated \b[<4-Bromobutan-1-ol>], for example as a <THP ether>. Convert the primary <bromide> to its <grignard reagent> and formylate with DMF, giving $\mathrm{THPOCH_2(CH_2)_3CHO}$. <olefination> with an allylidenetriphenylphosphorane, $\mathrm{Ph_3P=CHCH=CH_2}$, supplies a conjugated <diene> $\mathrm{THPOCH_2(CH_2)_3CH=CHCH=CH_2}$; select the required <diene> geometry rather than assume a single E/Z outcome.
Cycloaddition with methyl vinyl <ketone> produces a <cyclohexene> with a protected four-carbon <alcohol> chain at one saturated ring <carbon> and an acetyl group at its adjacent ring <carbon>. Choose and isolate the \b[adjacent-substituent cis regioisomer], matching the two dashed substituent bonds in the target. Endo preference and <diene> geometry can aid the selection, but an unsymmetrical <diene> is not guaranteed to give a unique regioisomer. Reduce the acetyl <ketone> to $\mathrm{CH(OH)Me}$, then methylate that <alcohol> with <sodium hydride>/methyl iodide while the chain-end OH is protected. Remove the THP group under mild acid conditions to reveal $\mathrm{Q(CH_2)_4OH}$, preserving the secondary methyl <ether> and the ring alkene.
Oxidize this primary <alcohol> to $\mathrm{Q(CH_2)_3CHO}$. Add vinylmagnesium <bromide> to give $\mathrm{Q(CH_2)_3CH(OH)CH=CH_2}$, then oxidize the allylic <alcohol> to the enone $\mathrm{Q(CH_2)_3C(=O)CH=CH_2}$. This <carbonyl> <carbon> is the original alcohol-end <carbon> of 4-bromobutanol; after <olefination> it will be the linker-bearing <carbon> of the left ring alkene.
In the other branch, reduce the specified <cyclopentanone> to cyclopentanol, convert to bromocyclopentane, and react with <triphenylphosphine> to obtain the cyclopentylphosphonium salt. Deprotonation gives the \b[cyclopentylidene phosphorane], whose ylidic <carbon> is part of the five-membered ring. Wittig <olefination> of the just-prepared enone gives the substituted <diene> displayed above. This <carbonyl>–<ylide> pairing keeps the ring <carbon> terminal in the <diene> and avoids accidentally constructing a fused ring instead of a spiro ring.
Finally, cycloadd an <ethylene equivalent>. Ethylene itself requires suitably forcing/high-pressure conditions; a more reactive alternative is <phenyl vinyl sulfone>, followed by reductive removal of the sulfone substituent using a method compatible with the methyl <ether> and retained C=C bonds. The latter installs the same two otherwise unsubstituted saturated carbons. Control or separate any additional cycloaddition isomers, and retain the previously selected cis configuration on $Q$.
The <carbon> count provides a strong check: <cyclopentanone> supplies five, bromobutanol four, DMF formylation one, the first allylidene <ylide> three, methyl vinyl <ketone> four, O-methylation one, vinylmagnesium two, and the final <ethylene equivalent> two, totalling \b[22 target carbons]. Three original bromobutanol carbons form the linker; its fourth becomes the substituted <carbon> of the spiro ring's alkene. The proposal is a multistep constitutional/relative-stereochemical route with explicit regioisomer and <diastereomer> selection, not an unsupported claim of a single quantitative cycloaddition product.
\Image[/past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1-q12-second-route.png]
{title=Original two-cycloaddition spiro synthesis with the four bromobutanol carbons mapped to the three-carbon linker and its adjacent alkene carbon}
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