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Karich is the modern Hebrew for sandwich. It is based on korech - the stage in the Seder when we eat bitter herbs between two pieces of matzah. The word korek derives from karach, which means to encircle, embrace or surround. Since this moment in the Haggadah is the closest thing to sandwich we have in Jewish liturgy, the revivers of Hebrew thought it would be an apt neologism.
In fact, Eliezer Ben Yehuda, the founder of modern Hebrew, at first wanted to call the sandwich a Hillelit, after Rabbi Hillel the Elder who innovated the matzah-maror sandwich in the Seder in emulation of the practice in the Temple of eating the Pesach sacrifice "on matzah and bitter herbs". As we say before eating it, "This is what Hillel used to do in memory of the Temple."
The cleverness of Ben Yehuda's suggestion was its imitation of the origin of the English word, sandwich, also named after its inventor, the Earl of Sandwich - such an inveterate gambler that he was unable to tear himself from the gaming table for lunch and so conceived the wheeze of putting a slab of meat between two slices of bread.
Hillelit never caught on. (If it had, we rabbis would never tire of pointing out how the English word was named after a gambling addict, while the Hebrew after a great sage.) Karich became common usage instead.
As Israel has westernized and sandwiches edge out falafel and shwarma as fast food, "sandvich" is competing with karich in everyday use. Ben Yehuda would not have been impressed.