A young pig, especially a piglet or a young domestic pig.
From Old Norse 'gríss,' meaning pig, which entered English through Scandinavian traders and settlers, remaining a regional or dialectal term in English.
Grice is one of those beautiful words that survived in certain English dialects because of geography—areas with Norse settlement kept Norse words for animals, which is why Scottish and Northern English farmers still sometimes call piglets 'grices.'
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