Etymology
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match-wood (n.)

also matchwood, 1590s, "wood used to start a fire;" 1838, "wood which has been split to proper size for matches," from match (n.1) + wood (n.). From the latter sense it has been used as a figure of speech for wood which has been broken or splintered into very small pieces. Also in this sense is matchsticks (1791).

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rat-a-tat (n.)

"a rattling sound or effect," 1680s, echoic, originally of a cooper hammering tubs.

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rat-race (n.)

also rat race, 1934 in reference to aviation training, from rat (n.) + race (n.1).

A rat race is ... a simple game of "follow the leader" in fighter planes. The leader does everything he can think of — Immelmanns, loops, snap rolls, and turns, always turns, tighter and tighter. [Popular Science, May 1941]

In the 1930s actual rat races of some sort are frequently mentioned among popular carnival and gambling attractions. Meaning "fiercely competitive struggle," especially to maintain one's position in work or life is by 1939. Rat-run is from 1870 in the sense of "maze-like passages by which rats move about their territory," but originally and usually in a derogatory transferred sense.

[Matthew] Milton was not, at the period we write of [c. 1811], at all in the ring ; for in the following March he was steward of a rat-race, held at a public-house in Shepherd's-market, where four of these "varmin," decorated with different coloured ribands, were started for a sweepstakes, round the clubroom, before a host of sportsmen. ["Sporting Incidents at Home and Abroad," The Sporting Review, May 1848]
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rat-catcher (n.)

"one whose business is the catching of rats, a ratter," 1590s, from rat (n.) + catcher.

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rat fink (n.)
also ratfink, 1963, teen slang, see rat (n.) + fink (n.). Popularized by, and perhaps coined by, U.S. custom car builder Ed "Big Daddy" Roth (1932-2001), who made a hot-rod comic character of it, supposedly to lampoon Mickey Mouse.
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rat-tail (n.)

also rat's-tail, from rat (n.) + tail (n.1). Used since 16c. of conditions, growths, or devices held to resemble a rat's long, hairless tail in any way, including "lank lock of hair" (1810); "end of a rope" (1867). Related: Rat-tailed. A rat-tail file (1744) is a fine, round file used for enlarging holes in metal.

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rat-snake (n.)

"snake which kills rats," 1818, from rat (n.) + snake (n.).

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rat-hole (n.)

also rathole, "the hole gnawed in woodwork, etc., by a rat or rats," 1812 first in the figurative sense of "nasty, messy place;" from rat (n.) + hole (n.). As "bottomless hole" (especially one where money goes) by 1921.

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rat-pack (n.)

1951, "a gang of disorderly young people" [OED], from rat (n.) + pack (n.). In reference to the Hollywood circle around Frank Sinatra, from 1958.

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rat-trap (n.)

"trap for catching rats," late 15c., rat trappe, from rat (n.) + trap (n.).

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