The most arch; most playfully mischievous, clever, or superior in manner.
Superlative form of 'arch,' which comes from Greek 'archi-' meaning 'chief' or 'principal.' Over time, 'arch' came to mean cleverly roguish or mischievous in tone.
When someone gives you 'the archest smile,' they're being so perfectly witty and superior that it's almost impossible to stay mad—it's the most cleverly cheeky expression you can make!
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