The compound adjective "three-day-old" is a modern English formation built from three foundational Germanic elements. The numeral "three" originates from the Proto-Indo-European root trei-, a stable numerical concept across Indo-European languages. "Day" descends from the Proto-Germanic dagaz, likely connected to the idea of heat or the sun's period. "Old" derives from the Proto-Germanic aldaz, conveying the core sense of grown, aged, or advanced in time. The compound's logic is transparently arithmetic and descriptive, combining a quantity of time units ("three day") with a state of having existed ("old") to precisely specify an age or freshness duration, a pattern commonly applied to infants, news, or perishable goods.

Structure: three (numeral) + day (noun) + old (adjective) - three: From Old English þrīe, þrēo, of Proto-Germanic origin; related to Dutch drie and German drei, from an Indo-European root shared by Latin tres and Greek treis. Functions as a numeral quantifier. - day: From Old English dæg, of Germanic origin; related to Dutch dag and German Tag. Functions as a noun denoting a 24-hour period. - old: From Old English ald, eald, of Germanic origin; related to Dutch oud and German alt. Functions as an adjective describing age or duration.