Scientific American:

The coin rotation paradox flummoxed SAT test writers even though we encounter this math problem every day

By Jack Murtagh on June 20, 2023

The 1982 SAT infamously held a math question so tricky that even its creators didn’t include a correct answer. The botch required the rescoring of 300,000 exams, scholastic victims of the knotty coin rotation paradox.
Here’s how the paradox works: Place two quarters flat on a table so that they are touching. Holding one coin stationary on the table, roll the other quarter around it, keeping edge contact between the two without slipping. When the moving quarter returns to its starting location, how many full rotations has it made? In other words, how many times has George Washington returned to his upright position in the graphic below? If you dig puzzles like this, take a minute to think about it.

Many people suspect that George will make one full rotation. A quarter’s circumference is about three inches around. So the moving quarter rolls along a path with a length of three inches, the same distance as its own circumference. If we wrap a string around a quarter and roll it along a three-inch path, unfurling the string as we go, then surely three inches of string will unfurl—just enough for a single rotation.

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