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Having had a lot of drinks, started to smoke (3,2)


I believe the answer is:

lit up

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'started to smoke' is the definition.
(I've seen this in another clue)

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for lit up that I've seen before include "like a bulb, perhaps?" , "Drunk (as a bulb?)" , "was illuminating" , "Drunk (informal)" , "bulb so transformed room?" .)

I've seen this clue in The Guardian and The Globe and Mail.
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