Etymology
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sixty (adj., n.)

"1 more than fifty-nine, twice thirty; the number which is one more than fifty-nine; a symbol representing this number;" Old English sixtig, from siex (see six) + -tig (see -ty (1)). Similar formation in Old Norse sextugr, sextögr, sextigir, Old Frisian sextich, Middle Dutch sestig, Dutch zestig, Old High German sehszug, German sechzig. Phrase sixty-four dollar question is attested from 1942, from a radio quiz show where that was the top prize.

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sixty-nine (adj., n.)

"1 more than sixty-eight; the number which is one more than sixty-eight; a symbol representing this number;" see sixty + nine. In the sexual sense, 1888, as a translation of French faire soixante neuf, literally "to do 69." So called from the similarity of positions to the arrangement of the numerals.

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sixtyfold 
also sixty-fold, Old English sixtigfeald; see sixty + -fold.
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sixtieth (adj., n.)

"next in order after the fifty-ninth; an ordinal numeral; being one of sixty equal parts into which a whole is regarded as divided;" Old English sixteogoða "sixtieth;" see sixty + -th (1).

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sixties (n.)
1848 as the years of someone's life between 60 and 69; 1827 as the seventh decade of years in a given century. See sixty.
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-ty (1)
suffix representing "ten" in cardinal numbers that are multiples of 10 (sixty, seventy, etc.), from Old English -tig, from a Germanic root (cognates: Old Saxon, Dutch -tig, Old Frisian -tich, Old Norse -tigr, Old High German -zug, German -zig) that existed as a distinct word in Gothic (tigjus) and Old Norse (tigir) meaning "tens, decades." Compare tithe (n.).

English, like many other Germanic languages, retains traces of a base-12 number system. The most obvious instance is eleven and twelve which ought to be the first two numbers of the "teens" series. Their Old English forms, enleofan and twel(eo)f(an), are more transparent: "leave one" and "leave two."

Old English also had hund endleofantig for "110" and hund twelftig for "120." One hundred was hund teantig. The -tig formation ran through 12 cycles, and could have bequeathed us numbers *eleventy ("110") and *twelfty ("120") had it endured, but already during the Anglo-Saxon period it was being obscured.

Old Norse used hundrað for "120" and þusend for "1,200." Tvauhundrað was "240" and þriuhundrað was "360." Older Germanic legal texts distinguished a "common hundred" (100) from a "great hundred" (120). This duodecimal system is "perhaps due to contact with Babylonia" [Lass, "Old English"].
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sexagenarian (n.)

1738, "person sixty years old or between sixty and seventy years old," from Latin sexagenarius "containing sixty," from sexagenarius, from sexageni "sixty each, sixty at a time," from sexaginta "sixty," from combining form of sex (see six). With -genaria "ten times," from -ginta "tens" (from PIE *dkm-ta-, from root *dekm- "ten"). As an adjective, "pertaining to or characteristic of the age from sixty to seventy," from 1836.

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sexagesimal (adj.)

"composed of or produced by sixties; pertaining to division into sixty," 1680s, from Medieval Latin sexagesimalis, from Latin sexagesimus "the sixtieth," from sexaginta "sixty." Sexagisema, "second Sunday before Lent" (eighth before Easter), is from late 14c. (Sexagesime), from Medieval Latin sexagesima (dies) "the sixtieth (day)."

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hemidemisemiquaver (n.)

"sixty-fourth note" in music, 1846, from hemi- + demi- + semi- + quaver (n.).

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shock (n.2)

"sheaves of grain placed on-end and leaning against one another in a field, arranged so as to shed rain and allow the grain to dry," early 14c., shok, perhaps from an unrecorded Old English word or from Middle Low German schok "shock of corn," originally "group of sixty," from Proto-Germanic *skukka- (source also of Old Saxon skok, Dutch schok "sixty pieces; shock of corn;" German schock "sixty," Hocke "heap of sheaves"). The original sense of this is uncertain; perhaps it is connected to the source of shock (n.1) on the notion of being "thrown" together [Century Dictionary]. The English word in 16c.-17c. sometimes was a unit of tale meaning "60-piece lot," from trade with the Dutch.

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