Update...
The Purdue Problem of the Week retired effective January 2019. The archives are still available with many problems to entertain and to illustrate a wide range of mathematical techniques.
About the Problem of the Week...
The Purdue Problem of the Week will has returned in a new, interactive format.
Problem of the Week is now a discussion board that functions similarly to StackExchange. Each Friday of the semester the problem will be posted on the webpage and will also appear in The Exponent. We will lock the associated discussion board for the first 24 hours to allow people time to read and ponder the problem.
After that time we will invite solutions to be posted on the discussion page and we strongly encourage people to post alternative solutions even when a good, existing solution has already been posted. The problems will remain of the same general type though we will occasionally have more advanced problems than what we have given in the past.
The discussion board for each problem will be moderated. Any user can post a solution. Users will be able to use MathJax to present their solutions and will also be able to vote up/down any solution and comment on any solution just like on StackExchange. We provide the problems, and you provide the solutions.
As Problem of the Week is strictly for entertainment purposes, we ask kindly that users work the problems themselves. Finding good problems is difficult and often problems (and solutions) can be found elsewhere on-line. We prefer problem of the week not test your ability to search the Internet.
About the founder of Problem of the Week
Michael Golomb, who passed away on April 9, 2008 at the age of 98, began the Problem of the Week program and ran it for many years. Several years prior to his passing, health problems forced him to stop administering the program, but he continued to provide the problems. And even now many of the problems appearing in Problem of the Week were provided by Michael Golomb. He created many of the problems himself, and collected (and often modified) the others from various sources.
For more information see Michael Golomb's obituary.