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Is it possible for a ketone like this to undergo the Wolf Kishner mechanism? If so, what would be the product? It seems unlikely to me as disrupting the stable equitorial carbonyl seems unfavorable...

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If you are thinking of reducing the ketone with hydrazine under alkaline conditions then I see a problem. The hydrazine will also act as a nucelophile on the alkyl bromide in the molecule. I think that you will have a SN2 reaction on the alkyl bromide to form an alkyl hydrazine at the same time as the hydrazine is reacting with the ketone. If you then heat it up with base you will remove the ketone but assuming that you use a large excess of hydrazine you will end up with an alkyl hydrazine in the top left of the molecule rather than an alkyl bromide.

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Why not react the original compound with benzyl alcohol using a mild base to form a benzyl ether at the start. Then do the reduction with hydrazine, then hydrogenate with hydrogen gas and palladium on carbon. This hydrogenation will remove the benzyl group and give you a alcohol. Then you can react the alcohol with tosyl chloride/pyridine and use the tosylate as an electrophile. If you very much want an alkyl bromide then react the tosylate with sodium bromide in DMF.

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