Maths for Testing Times.
Along with colleagues all over the world, I will be spending much of the next few weeks and months at home. Working — teaching, research, etc. — but detached. How best should I make use of the time? I will try to post more puzzles for students, and little notes that may be of interest to students or fellow educators.
For now, here is a little one: how many configurations are there of a 2x2x2 Rubik’s cube?
For our purposes, a ‘configuration’ is simply any position into which a ‘solved’ cube may be transformed by any finite sequence of the allowed physical twists.