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This 'Simple' Puzzle Once Stumped 96% of America's Top Math Students

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Twenty years ago, this puzzle appeared on a test administered to top-tier math students from 16 countries around the world. Only 10% of test takers got it right. In the U.S., only 4% managed to provide a correct response. Can you find the “simple” solution that so many intelligent students missed?

Earlier this week, a logic puzzle went viral. The riddle, which you can read here, challenged problem-solvers to determine someone’s birthday, based on what seemed, at first glance, to be insufficient information. I opted not to feature the brain teaser on io9, because – potential spoiler alert – I thought it too similar to another puzzle I posted here a few months ago. So why do I mention it at all? Two reasons.


Reason number one: It turns out the birthday riddle recently appeared on “a math olympiad test” for number-savvy high schoolers in Singapore. When I learned of the problem’s origins, I was immediately reminded of another puzzle, which, twenty years ago, bedeviled many of the world’s sharpest high-school-aged math students.

The puzzle in question appears below, exactly as it did on a test administered in 1995 to students in their final year of secondary school in 16 countries around the world. The test was one of three developed by the International Association for the Evaluation of Educational Achievement (IEA) to assess math and science literacy around the globe. Unlike the other two tests in the series, this one was designed specifically for final-year students who had taken advanced mathematics courses. The IEA later reported that this question stumped more students than almost any other on the exam. “Students in all participating countries found this problem very difficult,” reads the IEA’s Third International Mathematics and Science Report. “Only 10%, on average, provided a fully correct response, with another 2%, on average, receiving partial credit.” Swedish students fared best, with 24% providing full, correct answers. In the United States, just 4% of students were able to provide a complete solution.


Reason number two: I hesitate to provide the second reason. I worry it would provide too big a hint. I allude to it pretty directly above, in the headline and lede, but if you want a more explicit explanation, click here.

Art by Tara Jacoby

Sunday Puzzle #28: String Around the Rod

Image for article titled This 'Simple' Puzzle Once Stumped 96% of America's Top Math Students

We’ll be back next week with the solution – and a new puzzle! Got a great brainteaser, original or otherwise, that you’d like to see featured? E-mail me with your recommendations. (Be sure to include “Sunday Puzzle” in the subject line.)

UPDATE: The solution to Sunday Puzzle #28 has been posted.

SOLUTION To Sunday Puzzle #27: Finger Counting

Last week, I asked you to determine the highest number that could be reached by counting with the fingers on both hands (assuming, for the purposes of our puzzle, that thumbs are fingers, and that you are finger-counting with a total of ten digits).


The solution to this puzzle (or, at least, the solution I was looking for) is 1,023. The trick is to count not in base ten (which is how most of us learn to count on our fingers), but in base two. In this way, one can count as high as 31 using the digits on one hand, and as high as 1,023 using the digits on both hands. (Assuming they were nimble enough, you could use all your toes to count as high as 11111111111111111111 in binary, which translates to 1,048,575.)

Many of you arrived at the binary solution, above, but I was even more impressed with how many readers came up with ways to count even higher. Last week’s comments are full of solutions that involve using different hand positions to increase the maximum-countable-number multiple times over. Other commenters (who clearly possess more dexterity than I do), suggested using partial-finger (i.e. bent-finger) positioning to count in base three. Click here, then scroll down to the comments, to explore these alternate solutions.


Previous Weeks’ Puzzles