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It's not really a mistake in "calculation", but in the movie when he attempts to recite the Pythagorean Theorem after receiving his diploma, he mixes it up so that what he says is not actually true. It's never been clear to me whether this was a mistake in the script, a mistake by the actor, or if it's intentional to show that the Scarecrow isn't any smarter than he ever was.

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Q: What mistake in calculation did scarecrow make on wizard of oz?
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