This coin paradox problem, the hardest SAT math problem in history ever.

The problem is from 1st May 1982's test. It is reported that among 300 thousand who took the test around the world, only 3 got it right.

Even the maker of this problem also got it wrong—according to College Board, the standard answer is wrong, they had to make a statement and claimed that only 3 gave the real correct answer.

Mathematics scores are being recalculated for 300,000 students who took Scholastic Aptitude Tests around the nation on May 1 because three students proved there was a faulty answer, the College Board said yesterday.

Source: 25th May 1982, New York Times

Now let's look at the problem:

The radius of circle A is 1/3 of the radius of circle B. Circle A rolls around circle B one trip back to its starting point. How many times will circle A revolve in total?

A. 3/2 B. 3 C. 6 D. 9/2 E. 9

Nearly 300 thousand students answered "B.3". But the correct answer is actually "4", which is not in any of the five options.

This problem is called coin paradox.

The radius of circle A is 1/3 of the radius of circle B. That's why 300 thousand chose "3" as their answer.

But it is not the ratio of radius of circle A to the radius of circle B but the ratio of the center revolution radius of circle A to the radius of circle B that should be the correct answer, which is "4" in this problem.

General speaking, it's the ratio of radius of the green circle to radius of the small circle(circle A.)

The essence of the coin paradox is that the path drawn by each point of the revolution circle(ib this problem, it's circle A) is not a circle. For example, if the ratio of two circles is 2:1, the path will be a kidney shaped line.

If the radius of both circles are equal, it will be a heart shaped line

Unfortunately, most people, including the ones who made SAT test papers and chose this math problem, failed to see the essence of coin paradox, making this small multiple choice question the hardest math problem in whole SAT history.

Footnotes