It's not always easy to see how the mathematics of a problem connects to the problem itself.

In this post, with a little help from NumberPhile and Mills College mathematics professor Zvezdelina Stankova, you're going to learn about an unusual chessboard problem, and how the physical problem is turned into mathematics!

The problem starts with a chessboard that stretches off into infinity. A “prison” is marked off and some unusual rules are set, as explained in the following video. You might want to stop the video around the 3-minute mark, and try the challenge for yourself.



Now that you've got the basic idea of this puzzle, can you work out what would happen if you used different starting arrangements of clones? What about in “prisons” of different sizes? Professor Stankova continues with several variations in another related video:



After discussing how to handle variations, Professor Stankova then goes on to discuss a more general version of the problem, from which prisons can the clones escape, and from which ones can they NOT escape? You can read the original paper referred to in this third video online for free (PDF), if this problem is starting to grab your interest.

There's even a fourth video, largely consisting of footage excerpted from the first video above, in which Professor Stankova talks about how a problem is proved impossible when that happens to be the case.

Even if you don't find the particular problem intriguing, I still believe these videos are worth viewing in detail, as you get a good concept of overall problem solving and representing a problem mathematically in particular.