# Category Archives: problems and puzzles

## A Tantonalizing Problem

In times like these one craves distraction, or maybe anaesthesia. On the whole, mathematics is better for you than ethanol, and you can even do it while driving. So in spare moments I’ve been noodling away at the following problem, … Continue reading

## Lost in Translation

J. E. Littlewood told a cute story about a paper he supposedly published in the Comptes Rendus de l’AcadÃ©mie des sciences de Paris. The paper had three footnotes, which read, in French: I am greatly indebted to Prof. Riesz for … Continue reading

## 17 x 17 = $289.00

This just in from Bill Gasarch: The quest for a rectangle-free four-coloring of the 17-by-17 grid is over. If you don’t know what that’s all about, and you’d like to find out, see Bill’s blog post from 2009 or my … Continue reading

## 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