Blet: A Mathematical Puzzle
Fernando Rodríguez Villegas, Lorenzo Sadun, José Felipe Voloch · American Mathematical Monthly · 2002
this article we're going to spoil your fun by figuring out what the maximum number of heads is for any starting size, and devising a strategy for reaching that number. Before reading on, you might want to try solving the 10-coin puzzle (Blet-10) on your own. (You may prefer using a 2-color counter instead of coins. Or you can use pencil and paper. An electronic version, with 28 "coins" labeled 0 or 1, is available at http://www.ma.utexas.edu/users/voloch/blet.html). 2. Matrices and polygonal paths It's inconvenient to work with circular sequences, so we will pick a starting point, once and for all. Our configuration is then a word w in two symbols H and T , such as the example w = HTHHTTTH . (1) If the k-1-st, k-th and k+1-st letters are THT , we can convert them to HTH. We call this a "type-I" move,