Category Archives: problems and puzzles

Don’t try to read this proof!

On the subject of the Collatz conjecture (also known as the 3x+1 problem), Paul Erdos remarked: “Mathematics is not yet ready for such problems.” Shizuo Kakutani joked that the problem was a Cold War invention of the Russians meant to … Continue reading

Posted in mathematics, problems and puzzles | 4 Comments


Several weeks ago, on the morning after the first winter storm here in the Boston area, I wrote about some peculiar snow geometry on porch railings. Now, following another storm (which I wish I could believe might be the last … Continue reading

Posted in problems and puzzles, science | 4 Comments


It’s been almost a year since Bill Gasarch gave us the problem of four-coloring the nodes of a 17 × 17 grid in such a way that no rectangle has all four corners the same color. (See my earlier commentary … Continue reading

Posted in computing, mathematics, problems and puzzles | 2 Comments

Four questions about fuzzy rankings

The National Research Council is getting ready to release a new assessment of graduate-education programs in the U.S. The previous study, published in 1995, gave each Ph.D.-granting department a numerical score between 0 and 5, then listed all the programs … Continue reading

Posted in computing, games, mathematics, problems and puzzles, statistics | 22 Comments

A twist of fate

The school of philosophy called Antipodianism briefly flourished on the fringes of the Hellenistic world more than 2,000 years ago. The sect held that every person has an opposite number, a mirror image who inverts all our beliefs, feelings, actions … Continue reading

Posted in problems and puzzles | 6 Comments