# Category Archives: problems and puzzles

## Divisive diversions

The ever-puzzling Peter Winkler offered three problems in the August Communications of the ACM: Does every positive integer divide some number of the form 1{0,1}*—that is, a positive integer whose decimal representation includes no digits other than 0 and 1? … Continue reading

## 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

## Snowdunes

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

## Whack-a-Rectangle

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

## 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