Etymology
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one-upsmanship (n.)

"act or practice of being 'one up,'" 1952, from noun phrase one up "scoring one more point than one's opponent" (1919) + ending from sportsmanship, etc.

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one-act (adj.)

of a play, "consisting of a single act," 1888, from one + act (n.).

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one-stop (adj.)

1914, of airplane flights, "making a single stop along the way," from one + stop (n.). Of commercial establishments, "able to supply all of a customer's needs," by 1931. 

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one-horse (adj.)

"small-scale, petty" 1853, American English, colloquial, in reference to towns; see one + horse (n.). Probably from earlier use in reference to a carriage, sleigh, plow, etc., "drawn by a single horse" (1750); also "possessing only one horse" (of a farmer); hence "petty, on a small scale, of limited capacity or resources; inferior."

Shortly afterwards I took a stroll over the town. It was what is generally denominated a "one horse town," and I would think a pretty small pony at that. Two stores, one grocery, a stable, and four dwellings made up the sum of its buildings. ["Daguerreotyping in the Back Woods," in Yankee Notions, March, 1855]
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one-shot (adj.)
1907, "achieved in a single attempt" (original reference is to golf), from one + shot (n.). Meaning "happening or of use only once" is from 1937.
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one-way (adj.)

1824, "leading in one direction only;" by 1887 in reference to travel tickets or fares; 1914 in reference to streets; 1940 in reference to windows, mirrors, etc.; from one + way (n.).

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one-off (n.)

"single example of a manufactured product," by 1927, from one + off. Later given figurative extension.

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one-of-a-kind (adj.)

"unique," 1961, from the adverbial phrase; see one + kind (n.).

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cover-up (n.)

also coverup, "means or act of concealing" some event or activity, 1922, from the verbal phrase (1872), from cover (v.) + up (adv.).

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pop-up (n.)
from 1906 as a type of baseball hit; from pop (v.) + up (adv.). As an adjective from 1934 (of a children's book, later toasters, etc.).
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