A few weeks ago, Serhiy Grabarchuk sent me a problem involving matchstick snakes. The object is to find the longest snake that fits inside a certain area, without ever touching or crossing over itself. Like all great problems, I initially dismissed it. My first thought was that an infinite snake could be made, but then I reread his careful rule specification ... the angles the snake could bend at were limited. Recently, I started looking at the snakes bounded by a 2x2 square, and where all angles were multiples of 30 degrees. A lot of people, including me, spent some time studying these snakes, and many unexpected solutions popped up. One person, Susan Hoover, trounced all the rest of us with a delightful length 20 snake. As a puzzle, in a 2x2 square, put 20 matchsticks end to end so that all angles between two matchsticks are multiples of 30 degrees, and so that each matchstick only touches only those matches directly before or after it in the snake. I have the solution at my site. My own best solution was a 15-length snake. Some of my better solvers sent 17-length snakes, and then a few length 19 solutions trickled in. I have already started looking at other degree multiples, and other bounding areas. This looks like a rich problem. I haven't the foggiest idea what size of 20-degree snake will fit into a radius 2 circle, but I want to know. --Ed Pegg Jr, www.mathpuzzle.com