After 3 years perhaps this post requires a fresh look. An Olympiad question is unlikely to want to bog down a participant hunting for myriad rearrangements. Rather than obsess over rearrangements, perhaps one should start at the end of the problem where 1,3,5-cycloheptatriene (6) is the final product. The presence of a cycloheptane ring is not available in structures c and e. However, the remaining structures a, b and d do contain cycloheptane rings and are all candidates as structure C. What is required is the introduction of three double bonds, one by dehydration and two by successive Hofmann eliminations.
Achiral 1 is formed from a upon dehydration while rac-2 arises from b. Compound d leads to two possible alkenes, achiral 3 and rac-4. Bicyclic unsaturated amines 1 - 4 (structures J) are all candidates for successive Hofmann exhaustive eliminations. continued
Historical Note: One of the epimers of alcohol b is tropine, one of the components of atropine. The dehydration of b to alkene 2 and it subsequent oxidation leads to tropinic acid 6 (R=H). Its ester proved to be critical to the young career of Richard Wilstätter. When he performed a single exhaustive methylation on the ester, an ether soluble amine was obtained leading to the conclusion that tropine is a bridged amine. The text below is from his autobiography, From My Life, available through Amazon for the Kindle or online at the Hathi Trust, if you have access. A must read for both aspiring and accomplished chemists.