Penrose tilings are beautiful. They look spectacular, have a host of miraculous properties, and deep connections to fundamental areas of mathematics and computer science. And they also define funky grids on which we can reinvent a host of famous puzzles and games!
Peg solitaire is as simple as it is infuriating. Not least because when playing the infamous French variant, the game is impossible! But hidden just below the surface are some connections with linear programming, Diophantine equations, and the mysteriously named Fredholm alternative…
We all know that log(abc)=log(a)+log(b)+log(c). But when does log(a+b+c)=log(a)+log(b)+log(c)?
Can pi be approximated by counting the collisions between a pair of blocks sliding along a plane? Amazingly, yes! The setting for this post is the...