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No one is 100% sure, but Michael Quinion of World Wide Words offers the most thoroughly researched suggestion. According to Quinion, the phrase first appeared in American newspapers during the latter half of the 19th century. He notes that the phrase "in fine whack" had previously been used to describe something fit and sturdy. As John Hale describes Abraham Lincoln in 1863: "The Tycoon is in fine whack. I have rarely seen him more serene and busy. He is managing this war, the draft, foreign relations, and planning a reconstruction of the Union, all at once." So "out of whack" likely arose as an opposite to the saying "in fine whack." But whence the "whack"?
Quinion dates the word to the 18th century. Over the years it has had several different meanings: a whack on the head, a share of a thief's loot, a full price paid for something, or an attempt at doing something. Chrysti the Wordsmith from Wordsmith Radio points out the earlier definition of a "whack" as a share, bargain, or agreement. She posits that the word might be an onomatopoeia for the sound of an auctioneer's hammer's rap. In this sense, something that is "out of whack" would be "a bad bargain or an agreement that's gone awry." In other words, something that's out of kilter.
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