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at a loss is an adjective and adverb meaning "filled with bewilderment". It carries 2 recorded senses.
filled with bewilderment
“at a loss to understand those remarks”
“puzzled that she left without saying goodbye”
below cost
“sold the car at a loss”
Definitions, synonyms and semantic relations for at a loss come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.