The most typical New Year’s greeting in Germany is the slang phrase Einen guten Rutsch ins neue Jahr! or simply Guten Rutsch! These can be translated literally as “A good slide into the New Year!” or “Good slide!”
Dann wünsch' ich euch schöne Weihnachten,
In which case I wish you [plural] a wonderful Christmas,
'nen [einen] guten Rutsch ins neue Jahr und viel Spaß beim Anschauen. Tschüß!
a good slide to the new year and a lot of fun while watching. Bye!
Captions 84-85, Weihnachtsinterviews - Cettina in Linkenheim
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The word Rutsch means a downward sliding movement, and the greetings are meant to convey a smooth transition into the New Year, though the origin of the phrase is still uncertain. Let’s have a look at the more ordinary ways Rutsch and rutschen are used.
In an interview, Germany’s top windsurf star, Bernd Flessner, is asked if he can get from Altenteil Halpen to the Lighthouse in einem Rutsch durch (in one go [literally “through in one slide”]). The answer? Yes!
In einem Rutsch durch? -In einem Rutsch.
In one go? [literally “through in one slide”] -In one go.
Caption 9, Das "Race around Fehmarn" - Neuer Surfrekord
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A professor involves his talking pet bird named Dodo in demonstrating Newton's law of inertia using the “Dodomobil," (really just a shoebox). The verb rutschen (to slide or skid) is in more common usage than the noun Rutsch:
Dann... theoretisch, fährt dann das Dodomobil
Then… theoretically, the Dodomobile then continues to drive...
oder rutscht, besser gesagt...
or slide, rather…
rutscht das Dodomobil unendlich weiter.
the Dodomobile continues to slide infinitely.
Captions 38-39, Das 1. Newtonsche Gesetz - erklärt am Beispiel des Dodomobils
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Piggeldy and Frederick are playing on a Rutschbahn (a slide):
„Richtig", schrie Frederick und rutschte die Rutschbahn hinunter.
"Right," shouted Frederick and slid down the slide.
Caption 36, Piggeldy und Frederick - Spielen
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Watch out, Grandma! Here rutschen takes on another meaning:
Dann rutscht die Oma auf einer Bananenschale aus.
Then the grandmother slips on a banana peel.
Caption 13, Ivana erzählt Witze - Fritzle und die Oma
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So whether you are sliding down a slide, sliding into the New Year, or slipping on a banana peel, understanding this versatile word can help you have a guten Rutsch ins Deutsch!